change the exponential expression to an equivalent expression involving a logarithm. 8.8=7^x

please show work

ln 8.8 = x ln 7

x = ln 8.8 / ln 7

To change the exponential expression 8.8 = 7^x to an equivalent expression involving a logarithm, we can use the definition of a logarithm.

The definition states that if a^b = c, then log base a of c = b.

In this case, we have 8.8 = 7^x.

To rewrite this using logarithms, we take the logarithm of both sides of the equation.

log base 7 of 8.8 = log base 7 of 7^x

Using the power rule of logarithms, we can bring the x down as a coefficient:

log base 7 of 8.8 = x * log base 7 of 7

Since log base a of a = 1, we know that log base 7 of 7 equals 1, so we can simplify further:

log base 7 of 8.8 = x * 1

Finally, we get:

log base 7 of 8.8 = x

So the equivalent expression involving a logarithm is x = log base 7 of 8.8.

To change the exponential expression 8.8 = 7^x into an equivalent expression involving a logarithm, you need to take the logarithm of both sides of the equation. In this case, you can take the logarithm of base 7 on both sides of the equation.

Step 1: Take the logarithm of base 7 on both sides:
log₇(8.8) = log₇(7^x)

Step 2: Use a logarithmic property to rewrite the right side:
log₇(8.8) = x * log₇(7)

Step 3: Simplify the expression on the right side:
log₇(8.8) = x

Therefore, the equivalent expression involving a logarithm for the exponential expression 8.8 = 7^x is log₇(8.8) = x.