What is the solution in the equation 5^3x=700 ? Round your answer to the nearest hundredth.
To find the solution in the equation 5^(3x) = 700, we need to solve for x.
By taking the logarithm of both sides with base 5, we get:
log5(5^(3x)) = log5(700)
Using the logarithmic property, we can rewrite the left side of the equation as:
3x = log5(700)
Now, divide both sides of the equation by 3:
x = log5(700)/3
Using a calculator to approximate the value of log5(700)/3, we find x ≈ 3.33.
Therefore, the solution to the equation 5^(3x) = 700 rounded to the nearest hundredth is x ≈ 3.33.