\( \newcommand{\abs}[1]{\left| \, {#1} \, \right| } \) \( \newcommand{\cm}{\mathrm{cm} } \) \( \newcommand{\sec}{ \, \mathrm{sec} \, } \) \( \newcommand{\units}[1]{\,\text{#1}} \) \( \newcommand{\vhat}[1]{\,\hat{#1}} \) \( \newcommand{\vhati}{\,\hat{i}} \) \( \newcommand{\vhatj}{\,\hat{j}} \) \( \newcommand{\vhatk}{\,\hat{k}} \) \( \newcommand{\vect}[1]{\boldsymbol{\vec{#1}}} \) \( \newcommand{\norm}[1]{\|{#1}\|} \) \( \newcommand{\arccot}{ \, \mathrm{arccot} \, } \) \( \newcommand{\arcsec}{ \, \mathrm{arcsec} \, } \) \( \newcommand{\arccsc}{ \, \mathrm{arccsc} \, } \) \( \newcommand{\sech}{ \, \mathrm{sech} \, } \) \( \newcommand{\csch}{ \, \mathrm{csch} \, } \) \( \newcommand{\arcsinh}{ \, \mathrm{arcsinh} \, } \) \( \newcommand{\arccosh}{ \, \mathrm{arccosh} \, } \) \( \newcommand{\arctanh}{ \, \mathrm{arctanh} \, } \) \( \newcommand{\arccoth}{ \, \mathrm{arccoth} \, } \) \( \newcommand{\arcsech}{ \, \mathrm{arcsech} \, } \) \( \newcommand{\arccsch}{ \, \mathrm{arccsch} \, } \)

17Calculus Precalculus - Solve Logarithms

17Calculus
Single Variable Calculus
Derivatives
Integrals
Multi-Variable Calculus
Precalculus
Functions

Solving Equations Involving Logarithms

When we have a variable in an exponent, we need to move it out of the exponent to determine it's value. To do that, we use the laws listed on the laws of logarithm page. Also, if the variable is inside a logarithm, we use exponentials to get it out of the logarithm. Here is how it works.

Next

Okay, after working these practice problems, you will be ready to tackle some application problems involving exponentials and logarithms, starting with exponential growth and decay.

Trigonometry Demystified 2/E

Practice

Unless otherwise instructed, solve these problems using the exponential \(e\), giving your answers in exact terms.

Basic

\( \log_2(x+1) + \log_2(5x+1) = 6 \)

Problem Statement

Solve \( \log_2(x+1) + \log_2(5x+1) = 6 \)

Solution

3032 video solution

Log in to rate this practice problem and to see it's current rating.

\( \ln x = 7 \)

Problem Statement

Solve \( \ln x = 7 \)

Solution

3046 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log_3(10x+1) - \log_3(x+1) = 2 \)

Problem Statement

Solve \( \log_3(10x+1) - \log_3(x+1) = 2 \)

Solution

3034 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log_2 16 = x \)

Problem Statement

Solve \( \log_2 16 = x \)

Solution

3041 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log_x 81 = 4 \)

Problem Statement

Solve \( \log_x 81 = 4 \)

Solution

3042 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log_{32} x = 4/5 \)

Problem Statement

Solve \( \log_{32} x = 4/5 \)

Solution

3043 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log_3(5x+1) = 4 \)

Problem Statement

Solve \( \log_3(5x+1) = 4 \)

Solution

3044 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log x = 24 \)

Problem Statement

Solve \( \log x = 24 \)

Solution

3045 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log_7 (x^2+3x+9) = 2 \)

Problem Statement

Solve \( \log_7 (x^2+3x+9) = 2 \)

Solution

3047 video solution

Log in to rate this practice problem and to see it's current rating.

\( \ln(3x-2) = 5 \)

Problem Statement

Solve \( \ln(3x-2) = 5 \)

Solution

3048 video solution

Log in to rate this practice problem and to see it's current rating.

\( 4\ln(2x-1) + 3 = 11 \)

Problem Statement

Solve \( 4\ln(2x-1) + 3 = 11 \)

Solution

3049 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log_3 (5x+2) = \log_3 (7x-8) \)

Problem Statement

Solve \( \log_3 (5x+2) = \log_3 (7x-8) \)

Solution

3050 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log_2 (x^2+4x) = \log_2 (5) \)

Problem Statement

Solve \( \log_2 (x^2+4x) = \log_2 (5) \)

Solution

3051 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log_2 x + \log_2 (x+4) = 5 \)

Problem Statement

Solve \( \log_2 x + \log_2 (x+4) = 5 \)

Solution

3052 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log_3 (x+1) = 3 - \log_3 (x=7) \)

Problem Statement

Solve \( \log_3 (x+1) = 3 - \log_3 (x=7) \)

Solution

3053 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log_4 (2x+6) - \log_4 (x-1) = 1 \)

Problem Statement

Solve \( \log_4 (2x+6) - \log_4 (x-1) = 1 \)

Solution

3054 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log_2 (x+3) = 4 + \log_2 (x-3) \)

Problem Statement

Solve \( \log_2 (x+3) = 4 + \log_2 (x-3) \)

Solution

3055 video solution

Log in to rate this practice problem and to see it's current rating.

Advanced

\( \log x^{\log x} = 49 \)

Problem Statement

Solve \( \log x^{\log x} = 49 \)

Solution

3056 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log x^2 = (\log x)^2 \)

Problem Statement

Solve \( \log x^2 = (\log x)^2 \)

Solution

3057 video solution

Log in to rate this practice problem and to see it's current rating.

\( \log (\log x) = 4 \)

Problem Statement

Solve \( \log (\log x) = 4 \)

Solution

3058 video solution

Log in to rate this practice problem and to see it's current rating.

Really UNDERSTAND Precalculus

Log in to rate this page and to see it's current rating.

Topics You Need To Understand For This Page

basics of logarithms

laws of logarithms

To bookmark this page and practice problems, log in to your account or set up a free account.

Search Practice Problems

Do you have a practice problem number but do not know on which page it is found? If so, enter the number below and click 'page' to go to the page on which it is found or click 'practice' to be taken to the practice problem.

free ideas to save on books

Shop Amazon - Used Textbooks - Save up to 90%

As an Amazon Associate I earn from qualifying purchases.

I recently started a Patreon account to help defray the expenses associated with this site. To keep this site free, please consider supporting me.

Support 17Calculus on Patreon

Practice Search

Practice Instructions

Unless otherwise instructed, solve these problems using the exponential \(e\), giving your answers in exact terms.

Do NOT follow this link or you will be banned from the site!

When using the material on this site, check with your instructor to see what they require. Their requirements come first, so make sure your notation and work follow their specifications.

DISCLAIMER - 17Calculus owners and contributors are not responsible for how the material, videos, practice problems, exams, links or anything on this site are used or how they affect the grades or projects of any individual or organization. We have worked, to the best of our ability, to ensure accurate and correct information on each page and solutions to practice problems and exams. However, we do not guarantee 100% accuracy. It is each individual's responsibility to verify correctness and to determine what different instructors and organizations expect. How each person chooses to use the material on this site is up to that person as well as the responsibility for how it impacts grades, projects and understanding of calculus, math or any other subject. In short, use this site wisely by questioning and verifying everything. If you see something that is incorrect, contact us right away so that we can correct it.

Links and banners on this page are affiliate links. We carefully choose only the affiliates that we think will help you learn. Clicking on them and making purchases help you support 17Calculus at no extra charge to you. However, only you can decide what will actually help you learn. So think carefully about what you need and purchase only what you think will help you.

We use cookies on this site to enhance your learning experience.

17calculus

Copyright © 2010-2022 17Calculus, All Rights Reserved     [Privacy Policy]     [Support]     [About]

mathjax.org
Real Time Web Analytics