Solve for x, rounding to the nearest hundredth.
3^x/4=9
To solve for x, start by isolating the variable:
3^x/4 = 9
Multiply both sides of the equation by 4 to get rid of the fraction:
4 * (3^x/4) = 4 * 9
3^x = 36
Now, take the logarithm of both sides of the equation in order to bring x down from the exponent:
log (3^x) = log (36)
x log (3) = log (36)
To solve for x, divide both sides of the equation by log (3):
x = log (36) / log (3)
Using a calculator, evaluate the right side of the equation:
x ≈ 3.81
Therefore, x is approximately 3.81 when rounded to the nearest hundredth.