CPM Homework Help : INT3 Problem 8-21

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8-21.

Solve each equation.

$\operatorname { log } _ { 6 } ( x ) + \operatorname { log } _ { 6 } ( 5 ) = 3$
Step 1(a):
$\text{log}_{6}\left(5x\right) = 3$
Step 2(a):
$6^{3} = 5x$
Answer (a):
$x=\frac{216}{5}$

$\operatorname { log } _ { 7 } ( 7 ) - \operatorname { log } _ { 7 } ( x ) = 5$
Hint (b):
$\text{log}_{b}(m)-\text{log}_{b}(n)=\text{log}_{b}\left(\frac{m}{n}\right)$

$\operatorname { log } _ { 4 } ( 8 - x ) = \operatorname { log } _ { 4 } ( 6 )$
Step (c):
$8 − x = 6$ Why?

$\operatorname { log } _ { 5 } ( x ) - \operatorname { log } _ { 5 } ( 10 ) = \operatorname { log } _ { 5 } ( 2 )$
Hint (d):
Use the hint from part (b) and then the step from part (c).

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