what is the approximate value of x in the equation below? log₅15 = x + 3 -2.523 -1.317 2.880 7.485

Explanation:

Step1: Isolate x

Subtract 3 from both sides of the equation $\log_{5}15=x + 3$. So, $x=\log_{5}15-3$.

Step2: Use the change - of - base formula

The change - of - base formula for logarithms is $\log_{a}b=\frac{\ln b}{\ln a}$. Then $\log_{5}15=\frac{\ln15}{\ln5}$. We know that $\ln15\approx2.7081$ and $\ln5\approx1.6094$. So, $\frac{\ln15}{\ln5}=\frac{2.7081}{1.6094}\approx1.682$.

Step3: Calculate x

$x=\log_{5}15 - 3\approx1.682-3=-1.318\approx - 1.317$.

Answer:

-1.317