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

Given the equation:
`\log_{(3)/(4)} 25 = 3x-1`

Solve for x;

Use logarithmic rules:

`\log_b a = (\log a)/(\log b)`

Then;

`(\log 25)/(\log (3)/(4)) =3x-1`

Using values of:

`\log 25 = 1.39794001`

`\log (3)/(4) = -0.124938737`

Substitute these values we have;

`-(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_{(3)/(4)} 25 = 3x-1` is -3.396