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.