### Home > INT3 > Chapter 7 > Lesson 7.2.1 > Problem 7-58

7-58.

Compute the value of each expression without using a calculator. Homework Help ✎ log(8) + log(125)

log

_{25}(125)log(25) + log(20) 7

^{log}_{7}(12)

Use the Product Property of Logs:

log(*N*) + log(*M*) = log(*NM*).

log(8 · 125)

Remember you are working in log base 10.

log_{10}(1000)

3

Think of this in exponential form.

25^{?} = 125

Rewrite each side of the equation as a power of 5. The exponents are equal.

(5^{2})^{?} = 5^{3}

Apply the Power Property of Logs to the first logarithm and simplify.

log(5) + log(20)

Use the Product Property of Logs, as in part (a).

Let log_{7}(12) = *x*. Therefore the original expression becomes 7* ^{x}*. But 7

*= 12.*

^{x}