Question

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

Answer 1

Answer:

x = 2.16

Step-by-step explanation:

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

We have:

$4^x = 20$

Taking the natural logarithm of both sides:

$\ln(4^x) = \ln(20)$

Using the property of logarithms that $\ln(a^b) = b \cdot \ln(a)$, we get:

$x \cdot \ln(4) = \ln(20)$

Now, to isolate $x$, we divide both sides by $\ln(4)$:

$x = \dfrac{\ln(20)}{\ln(4)}$

Using a calculator:

$x \approx \dfrac{2.995732274}{1.386294361} \approx 2.160964047$

$x \approx 2.16 \textsf{(in nearest hundredth)}$

Therefore, the value of x is 2.16.