Answer:
Given the equation: [tex]\log_{\frac{3}{4}} 25 = 3x-1[/tex]
Solve for x;
Use logarithmic rules:
[tex]\log_b a = \frac{\log a}{\log b}[/tex]
Then;
[tex]\frac{\log 25}{\log \frac{3}{4}} =3x-1[/tex]
Using values of:
[tex]\log 25 = 1.39794001[/tex]
[tex]\log \frac{3}{4} = -0.124938737[/tex]
Substitute these values we have;
[tex]-\frac{1.39794001}{0.124938737} = 3x-1[/tex]
Simplify:
[tex]-11.1890039 =3x-1[/tex]
Add 1 to both sides we get;
-10.1890039 = 3x
Divide both sides by 3 we get;
[tex]x = - 3.39633463[/tex]
Therefore, the approximate value of x in the equation [tex]\log_{\frac{3}{4}} 25 = 3x-1[/tex] is -3.396
