3^(2x) = 14
and your question?
If it is to solve for x, take the log base 3 of each side.
2x=log3 14=2.40
To find the value of x in the equation 3^(2x) = 14, we need to use logarithms. Specifically, we can take the logarithm of both sides of the equation to rewrite it in a form that allows us to solve for x.
First, let's take the logarithm (base 3) of both sides of the equation:
log₃(3^(2x)) = log₃(14)
Using the property of logarithms, we can bring down the exponent 2x:
2x * log₃(3) = log₃(14)
Now, we know that log₃(3) is equal to 1, so we can simplify the equation further:
2x = log₃(14)
To isolate x, divide both sides of the equation by 2:
x = log₃(14) / 2
Now, you can either calculate log₃(14) using a calculator or use a change of base formula to evaluate the logarithm.
Using a calculator, you can directly calculate log₃(14) = 1.876.
Therefore, the approximate value of x in the equation 3^(2x) = 14 is x ≈ 0.938.