solve for x
75=13^x
take log of both sides
log 75 = log(13^x)
log 75 = x log 13
x = log75/log13 = appr 1.683
check:
13^1.683 = 74.949
(more accuracy attained when more accuracy is used in answer)
try x = 1.683264467 on your calculator
To solve for x in the equation 75 = 13^x, we need to isolate x.
Here are the steps to solve the equation:
Step 1: Take the logarithm of both sides of the equation. The choice of the logarithm base is arbitrary, but it is common to use the natural logarithm, ln (or log base 10, log).
ln(75) = ln(13^x)
Step 2: Use the power rule of logarithms to bring down the exponent in front.
ln(75) = x * ln(13)
Step 3: Divide both sides of the equation by ln(13) to solve for x.
x = ln(75) / ln(13)
Calculating the values:
Using a calculator, we can find the natural logarithms of 75 and 13.
ln(75) ≈ 4.3174881135
ln(13) ≈ 2.5649493575
Now, divide ln(75) by ln(13) to find x:
x ≈ 4.3174881135 / 2.5649493575 ≈ 1.6839721
Therefore, x ≈ 1.6839721 is the solution to the equation 75 = 13^x.