Question

question 11
your answer is incorrect.
solve for x: \\(6^x = 3\\)
a) \\(x = \log_3(6)\\)
b) \\(x = \ln(3)\\)
c) \\(x = \frac{1}{2}\\)
d) \\(x = \log_6(3)\\)
e) \\(x = \ln(2)\\)
f) none of the above.

Explanation:

Step1: Recall logarithm definition

For \(a^x = b\), \(x=\log_a(b)\) (by definition of logarithm).

Step2: Apply to given equation

Given \(6^x = 3\), using the logarithm definition, we get \(x = \log_6(3)\). Also, using change - of - base formula, \(x=\frac{\ln(3)}{\ln(6)}\), but the form \(\log_6(3)\) is a direct application of the logarithm definition for exponential equations.

Answer:

d) \(x=\log_6(3)\)