Question

Solve each logarithmic equation. Round your answer to two decimal places.

Answer 1

$\\ \rm\Rrightarrow 7log_9(x+8)=7$

$\\ \rm\Rrightarrow log_9(x+8)=1$

$\\ \rm\Rrightarrow x+8=9^1$

• a^1=a

$\\ \rm\Rrightarrow x+8=9$

$\\ \rm\Rrightarrow x=9-8$

$\\ \rm\Rrightarrow x=1$

Answer 2

Answer:

$\sf \boxed{\bold{x=1}}$

Explanation:

$\rightarrow \sf 7 log_9 (x + 8) = 7$

divide both sides by 7

$\rightarrow \sf \dfrac{7\log _9\left(x+8\right)}{7}=\dfrac{7}{7}$

simplify the following

$\sf \rightarrow \log _9\left(x+8\right)=1$

apply log rules                   $\underline{The \ rule}: \ \bold{log_{b} (a)= c} \ \ \Longrightarrow \sf a = b^c$

$\sf \rightarrow x+8 = 9^1$

simplify

$\sf \rightarrow x+8=9$

subtract both sides by 8

$\sf \rightarrow x=1$