### Home > CCA2 > Chapter 7 > Lesson 7.2.3 > Problem7-149

7-149.

Compute the value of each expression without using a calculator.

1. $\log\left(8\right) + \log\left(125\right)$

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

$\log(8 · 125)$

Remember you are working in log base $10$.

$\log_{10}(1000)$

$3$

1. $\log_{25}\left(125\right)$

Let the expression equal $x$ then convert to exponential form.

$25^{x} = 125$

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

$5^{2x} = 5^{3}$

1. $\frac { 1 } { 2 }\log(25) + \log(20)$

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

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

$\log\left(5\right) + \log\left(20\right)$

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

1. $7^{\log_7\left(12\right)}$

Remember the property that

$b^{\text{log}_b(N)} = N$