If 6^4x = 82, what is the value of x?
Typos?
6^4 = 72
To find the value of x in the equation 6^(4x) = 82, we need to isolate x using logarithms.
First, take the logarithm of both sides of the equation. You can use either the common logarithm (base 10) or the natural logarithm (base e). Let's use the natural logarithm in this case.
ln(6^(4x)) = ln(82)
Using the logarithmic property of exponents, we can bring down the exponent as a coefficient:
4x * ln(6) = ln(82)
Now, divide both sides of the equation by ln(6) to solve for x:
4x = ln(82) / ln(6)
Finally, divide both sides by 4 to get the value of x:
x = (ln(82) / ln(6)) / 4