Precalculus Examples

$2.1 e^{(\frac{x}{2}) \ln (3)} = 5$

Step 1

Divide both sides by $2.1 e^{(\frac{x}{2}) \ln (3)}$ to remove it from the front of the logarithm.

$\frac{2.1 e^{(\frac{x}{2}) \ln (3)}}{2.1 e^{(\frac{x}{2}) \ln (3)}} = \frac{5}{2.1 e^{(\frac{x}{2}) \ln (3)}}$

Step 2

Simplify each side of the equation.

$= \frac{2.\overline{380952}}{e^{\frac{x \ln (3)}{2}}}$

Step 3

For logarithmic equations, $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ such that $x > 0$ , $b > 0$ , and $b \neq 1$ . In this case, $b = 10$ , $x =$ , and $y = \frac{2.\overline{380952}}{e^{\frac{x \ln (3)}{2}}}$ .

$b = 10$

$x =$

$y = \frac{2.\overline{380952}}{e^{\frac{x \ln (3)}{2}}}$

Step 4

Substitute the values of $b$ , $x$ , and $y$ into the equation $b^{y} = x$ .