Question

Solve the following logarithmic equation, using a calculator if necessary to evaluate the logarithm. Write your answer as a fraction or round your answer to two decimal places. log7(2x−5)=2

Answer 1

The solution to the equation log7(2x - 5) = 2 is x = 27.

Explanation:

To solve the logarithmic equation log7(2x - 5) = 2, we can rewrite it in exponential form.

In exponential form, the equation becomes:

7^2 = 2x - 5

Simplifying the left side:

49 = 2x - 5

Adding 5 to both sides:

49 + 5 = 2x

54 = 2x

Dividing both sides by 2:

x = 54/2

x = 27

Therefore, the solution to the equation log7(2x - 5) = 2 is x = 27.