Solve f(x)=1/2(3)^x,text{when}x=5

$$f ( x ) = \frac { 1 } { 2 } ( 3 ) ^ { x } , \text { when } x = 5$$

Solve for f, x

$$x=5$$

$$f = \frac{243}{10} = 24\frac{3}{10} = 24.3$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$f\times 5=\frac{1}{2}\times 3^{5}$$

Calculate 3 to the power of 5 and get 243.

$$f\times 5=\frac{1}{2}\times 243$$

Multiply \frac{1}{2} and 243 to get \frac{243}{2}.

$$f\times 5=\frac{243}{2}$$

Divide both sides by 5.

$$f=\frac{\frac{243}{2}}{5}$$

Express \frac{\frac{243}{2}}{5} as a single fraction.

$$f=\frac{243}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$f=\frac{243}{10}$$

The system is now solved.

$$f=\frac{243}{10} x=5$$