How do you solve 1/125=25^6x-5
please and thank you
I read this as
1/125 = 256x-5
or
5-3=256x-5
Take the log base five of each side..
-3=2(6x-5) solve for x.
What exactly do you mean by take the log base five of each side?
Taking the log base five of each side means using the logarithm function with a base of five to find the exponent needed to raise the base (in this case, five) to obtain the given value.
In the equation 5^(-3) = 25^(6x-5), we can rewrite it as logbase5(5^(-3)) = logbase5(25^(6x-5)).
Applying the log base five function to both sides converts the exponential equation into a logarithmic equation. The logarithm base five of 5^(-3) is -3, and the logarithm base five of 25^(6x-5) is (6x-5).
So, the equation becomes -3 = 6x-5. From here, we can solve for x by isolating the variable x.
Adding 5 to both sides of the equation gives us -3 + 5 = 6x, which simplifies to 2 = 6x.
Finally, dividing both sides of the equation by 6 yields x = 2/6 or x = 1/3 as the solution.