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.
8^x=3√5

Answer 1

Answer:

x = 0.92

Step-by-step explanation:

To solve the equation $8^x = 3\sqrt{5}$ using logarithms, we can take the logarithm of both sides. Specifically, we'll use the natural logarithm (ln) to maintain consistency.

Given:

$8^x = 3\sqrt{5}$

Taking the natural logarithm of both sides:

$\ln(8^x) = \ln(3\sqrt{5})$

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

$x \cdot \ln(8) = \ln(3\sqrt{5})$

Now, to isolate $x$, we divide both sides by $\ln(8)$:

$x = \dfrac{\ln(3\sqrt{5})}{\ln(8)}$

Using a calculator:

$x \approx \dfrac{1.903331245}{ 2.079441542}$

$x \approx 0.9153088494$

$x \approx 0.92 \textsf{(in nearest hundredth)}$

Therefore, the value of x is 0.92.