solve the following exponential equation.
7^x=8
a. x= Write in exact solution
b. then with that answer move the decimal 3 points over
log10(7^x) = log10(8)
Using log rules (log(a^b) = b*log(a))
x*log10(7) = log10(8)
x*.845 = .903 = log(8)/log(7)
x = 1.068 to 3 decimals
To solve the exponential equation 7^x = 8, we need to isolate the variable x. Here's how you can do it:
a. Write the equation: 7^x = 8
Take the logarithm (log) of both sides of the equation. Any base can be used, but it is common to use either the natural logarithm (ln) or the common logarithm (log base 10).
b. Using natural logarithm (ln):
ln(7^x) = ln(8)
Apply the logarithmic property for exponents: ln(a^b) = b * ln(a)
x * ln(7) = ln(8)
Now, divide both sides by ln(7) to isolate x:
x = ln(8) / ln(7)
Using a calculator to evaluate ln(8) and ln(7), you can find an approximate value for x.
c. To move the decimal point three places over from the obtained answer, you can use multiplication. Take the answer from step b and multiply it by 1000.
So, x (after moving the decimal 3 points over) = x * 1000
Remember to use the exact value from step b, rather than any rounded or approximate value.