Solve: 3log₄(9) + 8log₄(1/3) Logarithmic Expression

Question

$3\log_49+8\log_4\frac{1}{3}=$

00:00 Solve

00:06 We will use the formula for log of power

00:20 We will use this formula in our exercise

00:36 Let's solve each power separately

00:52 We will use the formula for adding logarithms

01:03 We will use this formula in our exercise

01:21 Let's calculate the fraction

01:32 Convert from fraction to negative power

01:35 And again we'll use the formula for log of power

01:40 And this is the solution to the question

Where:

$3\log_49=\log_49^3=\log_4729$

$8\log_4\frac{1}{3}=\log_4\left(\frac{1}{3}\right)^8=$

$\log_4\frac{1}{3^8}=\log_4\frac{1}{6561}$

Therefore

$3\log_49+8\log_4\frac{1}{3}=$

$\log_4729+\log_4\frac{1}{6561}$

$\log_ax+\log_ay=\log_axy$

$\left(729\cdot\frac{1}{6561}\right)=\log_4\frac{1}{9}$

$\log_49^{-1}=-\log_49$

$-\log_49$