Evaluate Using the Given Value log base 3/4 of 25=3x-1

$\log_{\frac{3}{4}} (25) = 3 x - 1$

Step 1

Rewrite the equation as $3 x - 1 = \log_{\frac{3}{4}} (25)$ .

$3 x - 1 = \log_{\frac{3}{4}} (25)$

Step 2

Add $1$ to both sides of the equation.

$3 x = \log_{\frac{3}{4}} (25) + 1$

Step 3

Divide each term in $3 x = \log_{\frac{3}{4}} (25) + 1$ by $3$ and simplify.

Divide each term in $3 x = \log_{\frac{3}{4}} (25) + 1$ by $3$ .

$\frac{3 x}{3} = \frac{\log_{\frac{3}{4}} (25)}{3} + \frac{1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{\log_{\frac{3}{4}} (25)}{3} + \frac{1}{3}$

Divide $x$ by $1$ .

$x = \frac{\log_{\frac{3}{4}} (25)}{3} + \frac{1}{3}$

Simplify the right side.

Simplify each term.

Rewrite $\frac{\log_{\frac{3}{4}} (25)}{3}$ as $\frac{1}{3} \log_{\frac{3}{4}} (25)$ .

$x = \frac{1}{3} \log_{\frac{3}{4}} (25) + \frac{1}{3}$

Simplify $\frac{1}{3} \log_{\frac{3}{4}} (25)$ by moving $\frac{1}{3}$ inside the logarithm.

$x = \log_{\frac{3}{4}} (25^{\frac{1}{3}}) + \frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \log_{\frac{3}{4}} (25^{\frac{1}{3}}) + \frac{1}{3}$

Decimal Form:

$x = - 3.39633462 \dots$