Question

solve the exponential equation.\\(0.3^x = 8\\)\
select the correct choice below and, if necessary, fill in the answer box to complete your choice.\
\\(\boldsymbol{\circ}\\) a. the solution set is \\(\\{-1.7277\\}\\).\
\\(\quad\\) (round to four decimal places as needed. use a comma to separate answers as needed.)\
\\(\boldsymbol{\circ}\\) b. the solution is the empty set.

Explanation:

Step1: Take log of both sides

$\log(0.3^x) = \log(8)$

Step2: Apply log power rule

$x\log(0.3) = \log(8)$

Step3: Isolate x

$x = \frac{\log(8)}{\log(0.3)}$

Step4: Calculate and round

$x \approx \frac{0.903089987}{-0.5228787453} \approx -1.7277$

Answer:

A. The solution set is $\{-1.7277\}$
(Round to four decimal places as needed. Use a comma to separate answers as needed.)