An aproximation for the solution of the logarithmic equation is:
x = 0.304.
Solving logarithmic equations.
Here we want to solve:
[tex]log_{25}(3/4) = 3x - 1[/tex]
Remember that we can rewrite the logarithm as the quotient of two natural logarithms, so we get:
[tex]log_{25}(3/4) = ln(3/4)/ln(25)[/tex]
And the natural logarithm of a quotient is equal to the difference between the logarithms of the numerator and denominator, using that we get:
[tex]\frac{ln(3) - ln(4)}{ln(25)} = 3x - 1\\\\x = (1 + \frac{ln(3) - ln(4)}{ln(25)})/3[/tex]
Now we can solve this directly, we will get:
x = 0.304
If you want to learn more about logarithms, you can read:
https://brainly.com/question/13473114
