Question

question 10
solve for ( x ): ( 6^x = 53 )
the exact solution (using logarithms) is: ( x = )
the approximate answer, rounded to 4 decimal places, is: ( x = )
question help: (\boxed{\text{video}}) (\boxed{\text{submit question}})

Explanation:

Step1: Take log of both sides

$\log(6^x) = \log(53)$

Step2: Apply log power rule

$x\log(6) = \log(53)$

Step3: Isolate x (exact form)

$x = \frac{\log(53)}{\log(6)}$

Step4: Calculate decimal approximation

$x \approx \frac{1.7242758696}{0.7781512504} \approx 2.2158$

Answer:

Exact solution: $x = \frac{\log(53)}{\log(6)}$
Approximate solution: $x = 2.2158$