Answer:
[tex]\boxed {x = log_{3} (14)}[/tex]
Step-by-step explanation:
-To solve this, use the rules of the exponents and the logarithms:
[tex]3^{x} - 5 = 9[/tex]
-Add [tex]5[/tex] from both sides:
[tex]3^{x} - 5 + 5 = 9 + 5[/tex]
[tex]3^{x} = 14[/tex]
-Take the logarithm to both sides:
[tex]3^{x} = 14[/tex]
[tex]log(3^{x}) = log(14)[/tex]
-Divide both sides by [tex]log(3)[/tex] and by the change of base formula, [tex]\frac{log(a)}{log(b)} = log_{b} (a)[/tex]:
[tex]\frac{log(14)}{log(3)}[/tex]
[tex]\boxed {x = log_{3} (14)}[/tex]
Therefore, the solution is [tex]x = log_{3} (14)[/tex].
