How to find

(7.27)^x=86.8

To find the value of x in the equation (7.27)^x = 86.8, we can use logarithms. Logarithms help us solve exponential equations like this one.

Step 1: Take the logarithm of both sides of the equation. You can use any base for the logarithm, but the most common bases are 10 (log) and the natural logarithm (ln) with base e.

If we use the natural logarithm (ln), we get:
ln[(7.27)^x] = ln(86.8)

Step 2: Apply the logarithmic property that states ln(a^b) = b * ln(a) to simplify the left side:
x * ln(7.27) = ln(86.8)

Step 3: Divide both sides of the equation by ln(7.27) to solve for x:
x = ln(86.8) / ln(7.27)

Step 4: Use a calculator to evaluate the division of natural logarithms and find the value of x.

By substituting ln(86.8) and ln(7.27) into the equation, we can calculate the value of x.