### Home > INT3 > Chapter 7 > Lesson 7.2.1 > Problem7-58

7-58.
1. Compute the value of each expression without using a calculator. Homework Help ✎

1. log(8) + log(125)

2. log25(125)

3. log(25) + log(20)

4. 7log7(12)

Use the Product Property of Logs:
log(N) + log(M) = log(NM).

log(8 · 125)

Remember you are working in log base 10.

log10(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.

(52)? = 53

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

$\log (25)^{1/2} + \log (20)$

log(5) + log(20)

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

Let log7(12) = x. Therefore the original expression becomes 7x. But 7x = 12.