Solve for x 26*3^(x/4)=25

$26 \cdot 3^{\frac{x}{4}} = 25$

Step 1

Divide each term in $(26 \cdot 3^{\frac{x}{4}}) = 25$ by $26$ and simplify.

Divide each term in $(26 \cdot 3^{\frac{x}{4}}) = 25$ by $26$ .

$\frac{(26 \cdot 3^{\frac{x}{4}})}{26} = \frac{25}{26}$

Simplify the left side.

Cancel the common factor of $26$ .

Cancel the common factor.

$\frac{26 \cdot 3^{\frac{x}{4}}}{26} = \frac{25}{26}$

Divide $3^{\frac{x}{4}}$ by $1$ .

$3^{\frac{x}{4}} = \frac{25}{26}$

Step 2

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (3^{\frac{x}{4}}) = \ln (\frac{25}{26})$

Step 3

Expand the left side.

Expand $\ln (3^{\frac{x}{4}})$ by moving $\frac{x}{4}$ outside the logarithm.

$\frac{x}{4} \ln (3) = \ln (\frac{25}{26})$

Combine $\frac{x}{4}$ and $\ln (3)$ .

$\frac{x \ln (3)}{4} = \ln (\frac{25}{26})$

Step 4

Multiply both sides of the equation by $\frac{4}{\ln (3)}$ .

$\frac{4}{\ln (3)} \cdot \frac{x \ln (3)}{4} = \frac{4}{\ln (3)} \ln (\frac{25}{26})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{\ln (3)} \cdot \frac{x \ln (3)}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{\ln (3)} \cdot \frac{x \ln (3)}{4} = \frac{4}{\ln (3)} \ln (\frac{25}{26})$

Rewrite the expression.

$\frac{1}{\ln (3)} (x \ln (3)) = \frac{4}{\ln (3)} \ln (\frac{25}{26})$

Cancel the common factor of $\ln (3)$ .

Factor $\ln (3)$ out of $x \ln (3)$ .

$\frac{1}{\ln (3)} (\ln (3) x) = \frac{4}{\ln (3)} \ln (\frac{25}{26})$

Cancel the common factor.

$\frac{1}{\ln (3)} (\ln (3) x) = \frac{4}{\ln (3)} \ln (\frac{25}{26})$

Rewrite the expression.

$x = \frac{4}{\ln (3)} \ln (\frac{25}{26})$

Simplify the right side.

Combine $\frac{4}{\ln (3)}$ and $\ln (\frac{25}{26})$ .

$x = \frac{4 \ln (\frac{25}{26})}{\ln (3)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4 \ln (\frac{25}{26})}{\ln (3)}$

Decimal Form:

$x = - 0.14280092 \dots$

Solve for x 26*3^(x/4)=25

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