Solve for x 4^(0.2x)+6=43

$4^{0.2 x} + 6 = 43$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$4^{0.2 x} = 43 - 6$

Subtract $6$ from $43$ .

$4^{0.2 x} = 37$

Step 2

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

$\ln (4^{0.2 x}) = \ln (37)$

Step 3

Expand the left side.

Expand $\ln (4^{0.2 x})$ by moving $0.2 x$ outside the logarithm.

$0.2 x \ln (4) = \ln (37)$

Multiply $\ln (4)$ by $0.2$ .

$0.27725887 x = \ln (37)$

Step 4

Divide each term in $0.27725887 x = \ln (37)$ by $0.27725887$ and simplify.

Divide each term in $0.27725887 x = \ln (37)$ by $0.27725887$ .

$\frac{0.27725887 x}{0.27725887} = \frac{\ln (37)}{0.27725887}$

Simplify the left side.

Cancel the common factor of $0.27725887$ .

Cancel the common factor.

$\frac{0.27725887 x}{0.27725887} = \frac{\ln (37)}{0.27725887}$

Divide $x$ by $1$ .

$x = \frac{\ln (37)}{0.27725887}$

Simplify the right side.

Replace $e$ with an approximation.

$x = \frac{\log_{2.71828182} (37)}{0.27725887}$

Log base $2.71828182$ of $37$ is approximately $3.61091791$ .

$x = \frac{3.61091791}{0.27725887}$

Divide $3.61091791$ by $0.27725887$ .

$x = 13.02363341$