Question

What is the approximate value of x in the equation below. log 3/4 25 =3x-1

Answer 1

Solve for x by simplifying both sides od the equation, then isolating the variable.

x=79/12

Answer 2

Answer:

Given the equation: $\log_{\frac{3}{4}} 25 = 3x-1$

Solve for x;

Use logarithmic rules:

$\log_b a = \frac{\log a}{\log b}$

Then;

$\frac{\log 25}{\log \frac{3}{4}} =3x-1$

Using values of:

$\log 25 = 1.39794001$

$\log \frac{3}{4} = -0.124938737$

Substitute these values we have;

$-\frac{1.39794001}{0.124938737} = 3x-1$

Simplify:

$-11.1890039 =3x-1$

Add 1 to both sides we get;

-10.1890039 = 3x

Divide both sides by 3 we get;

$x = - 3.39633463$

Therefore, the approximate  value of x in the equation  $\log_{\frac{3}{4}} 25 = 3x-1$ is -3.396