Question

solve the equation. round your answers to the nearest ten - thousandth.
$4^x = 99$
a 3.3147
b 4.5951
c 1.9956
d no solution.

Explanation:

Step1: Take log of both sides

Take the logarithm (natural log or common log) of both sides of the equation \(4^x = 99\). Using natural logarithm (ln) for this, we get \(\ln(4^x)=\ln(99)\).

Step2: Apply logarithm power rule

By the power rule of logarithms, \(\ln(a^b)=b\ln(a)\), so the left - hand side becomes \(x\ln(4)=\ln(99)\).

Step3: Solve for x

We can solve for \(x\) by dividing both sides of the equation \(x\ln(4)=\ln(99)\) by \(\ln(4)\). So \(x = \frac{\ln(99)}{\ln(4)}\).
Now, calculate the values: \(\ln(99)\approx4.5951197\) and \(\ln(4)\approx1.3862944\). Then \(x=\frac{4.5951197}{1.3862944}\approx3.3147\).

Answer:

A. 3.3147