For each equation solve one of them by using powers of the same number.to the nearest hundredth, solve the other by using logarithms. 4^x=20

To solve the equation [tex]4^x = 20[/tex] using logarithms, we'll take the logarithm of both sides. Specifically, we'll use the natural logarithm (ln) to maintain consistency.

We have:

[tex]4^x = 20[/tex]

Taking the natural logarithm of both sides:

[tex] \ln(4^x) = \ln(20) [/tex]

Using the property of logarithms that [tex] \ln(a^b) = b \cdot \ln(a) [/tex], we get:

[tex] x \cdot \ln(4) = \ln(20) [/tex]

Now, to isolate [tex]x[/tex], we divide both sides by [tex]\ln(4)[/tex]:

[tex] x = \dfrac{\ln(20)}{\ln(4)} [/tex]

Using a calculator:

[tex] x \approx \dfrac{2.995732274}{1.386294361} \approx 2.160964047 [/tex]

[tex] x \approx 2.16 \textsf{(in nearest hundredth)}[/tex]

Therefore, the value of x is 2.16.