Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.%0D%0A%0D%0AEvaluate the logarithm.%0D%0A%0D%0A log6136

Answer 1

To evaluate the logarithm of 136 to the base 6, we need to find the exponent to which we raise 6 to get 136.

In other words, we need to solve the equation:

6^x = 136

To solve this equation, we can use the fact that 6^2 = 36 and 6^3 = 216.

Since 136 is between 36 and 216, we can estimate that the exponent must be between 2 and 3.

To get a more precise answer, we can use trial and error. We can try different values for x, such as 2.5:

6^2.5 = 36^(1/2) * 36 = 6 * 36 = 216

Since 216 is greater than 136, we know that 2.5 is too large.

We can now try a smaller value, such as 2.4:

6^2.4 = 36^(1/2) * 6 = 6 * 6 = 36

Since 36 is less than 136, we know that 2.4 is too small.

By continuing this process and narrowing down the range, we can find that the exponent x is approximately 2.58.

Therefore, the logarithm of 136 to the base 6 is approximately 2.58.