Question

solve. round your answer to the nearest thousandth.
19 = 9^x
x =

Explanation:

Step1: Take log of both sides

To solve for \( x \) in the equation \( 19 = 9^x \), we take the logarithm of both sides. Using the natural logarithm (ln) for this, we get:
\( \ln(19) = \ln(9^x) \)

Step2: Apply logarithm power rule

By the power rule of logarithms, \( \ln(a^b)=b\ln(a) \), so we can rewrite the right - hand side as:
\( \ln(19)=x\ln(9) \)

Step3: Solve for x

Now, we solve for \( x \) by dividing both sides of the equation by \( \ln(9) \):
\( x = \frac{\ln(19)}{\ln(9)} \)

Step4: Calculate the value

We know that \( \ln(19)\approx2.944438979 \) and \( \ln(9)\approx2.197224577 \). Then:
\( x=\frac{2.944438979}{2.197224577}\approx1.340 \) (rounded to the nearest thousandth)

Answer:

\( 1.340 \)