Solve for x 3*2^(x/5)=150

$3 \cdot 2^{\frac{x}{5}} = 150$

Step 1

Divide each term in $(3 \cdot 2^{\frac{x}{5}}) = 150$ by $3$ and simplify.

Divide each term in $(3 \cdot 2^{\frac{x}{5}}) = 150$ by $3$ .

$\frac{(3 \cdot 2^{\frac{x}{5}})}{3} = \frac{150}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 \cdot 2^{\frac{x}{5}}}{3} = \frac{150}{3}$

Divide $2^{\frac{x}{5}}$ by $1$ .

$2^{\frac{x}{5}} = \frac{150}{3}$

Simplify the right side.

Divide $150$ by $3$ .

$2^{\frac{x}{5}} = 50$

Step 2

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

$\ln (2^{\frac{x}{5}}) = \ln (50)$

Step 3

Expand the left side.

Expand $\ln (2^{\frac{x}{5}})$ by moving $\frac{x}{5}$ outside the logarithm.

$\frac{x}{5} \ln (2) = \ln (50)$

Combine $\frac{x}{5}$ and $\ln (2)$ .

$\frac{x \ln (2)}{5} = \ln (50)$

Step 4

Multiply both sides of the equation by $\frac{5}{\ln (2)}$ .

$\frac{5}{\ln (2)} \cdot \frac{x \ln (2)}{5} = \frac{5}{\ln (2)} \ln (50)$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{\ln (2)} \cdot \frac{x \ln (2)}{5}$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5}{\ln (2)} \cdot \frac{x \ln (2)}{5} = \frac{5}{\ln (2)} \ln (50)$

Rewrite the expression.

$\frac{1}{\ln (2)} (x \ln (2)) = \frac{5}{\ln (2)} \ln (50)$

Cancel the common factor of $\ln (2)$ .

Factor $\ln (2)$ out of $x \ln (2)$ .

$\frac{1}{\ln (2)} (\ln (2) x) = \frac{5}{\ln (2)} \ln (50)$

Cancel the common factor.

$\frac{1}{\ln (2)} (\ln (2) x) = \frac{5}{\ln (2)} \ln (50)$

Rewrite the expression.

$x = \frac{5}{\ln (2)} \ln (50)$

Simplify the right side.

Combine $\frac{5}{\ln (2)}$ and $\ln (50)$ .

$x = \frac{5 \ln (50)}{\ln (2)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5 \ln (50)}{\ln (2)}$

Decimal Form:

$x = 28.21928094 \dots$

Solve for x 3*2^(x/5)=150

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