## 17Calculus Precalculus - Solve Logarithms

##### 17Calculus

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.

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

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$$\ln x = 7$$

Problem Statement

Solve $$\ln x = 7$$

Solution

### 3046 video solution

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

Problem Statement

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

Solution

### 3034 video solution

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$$\log_2 16 = x$$

Problem Statement

Solve $$\log_2 16 = x$$

Solution

### 3041 video solution

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$$\log_x 81 = 4$$

Problem Statement

Solve $$\log_x 81 = 4$$

Solution

### 3042 video solution

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$$\log_{32} x = 4/5$$

Problem Statement

Solve $$\log_{32} x = 4/5$$

Solution

### 3043 video solution

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

Problem Statement

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

Solution

### 3044 video solution

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$$\log x = 24$$

Problem Statement

Solve $$\log x = 24$$

Solution

### 3045 video solution

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

Problem Statement

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

Solution

### 3047 video solution

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

Problem Statement

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

Solution

### 3048 video solution

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

Problem Statement

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

Solution

### 3049 video solution

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

Problem Statement

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

Solution

### 3050 video solution

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

Problem Statement

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

Solution

### 3051 video solution

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

Problem Statement

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

Solution

### 3052 video solution

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

Problem Statement

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

Solution

### 3053 video solution

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

Problem Statement

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

Solution

### 3054 video solution

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

Problem Statement

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

Solution

### 3055 video solution

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$$\log x^{\log x} = 49$$

Problem Statement

Solve $$\log x^{\log x} = 49$$

Solution

### 3056 video solution

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

Problem Statement

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

Solution

### 3057 video solution

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

Problem Statement

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

Solution

### 3058 video solution

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