Question

question 2 of 10
what is the solution to the equation below? round your answer to two decimal places.
$6^x = 66$
a. $x = 1.04$
b. $x = 0.43$
c. $x = 2.34$
d. $x = 2.40$

Explanation:

Step1: Take log of both sides

To solve \(6^x = 66\), take the logarithm (natural or common) of both sides. Using natural logarithm: \(\ln(6^x)=\ln(66)\)

Step2: Apply log power rule

Using the power rule of logarithms (\(\ln(a^b)=b\ln(a)\)), we get \(x\ln(6)=\ln(66)\)

Step3: Solve for x

Divide both sides by \(\ln(6)\): \(x = \frac{\ln(66)}{\ln(6)}\)

Step4: Calculate the value

Using a calculator, \(\ln(66)\approx4.1897\) and \(\ln(6)\approx1.7918\). Then \(x=\frac{4.1897}{1.7918}\approx2.34\)

Answer:

C. \(x = 2.34\)