Solving Exponential and Logarithmic Equations

For symbolic solutions to exponential or logarithmic equations, from the Solve submenu, choose Exact. Enter Variable(s) to Solve for if requested. For numerical solutions, you can either enter a coefficient in decimal notation and choose Solve + Exact, or apply Evaluate Numerically to the symbolic solutions. In the case of a single variable, you can choose Solve + Numeric.

$\blacktriangleright$ Solve + Exact

3x = 8, Solution is : $\left\{\vphantom{ x=\frac{\ln 8}{\ln 3}}\right.$x = ${\frac{{\ln 8}}{{\ln 3}}}$$\left.\vphantom{ x=\frac{\ln 8}{\ln 3}}\right\}$

ex = ${\dfrac{{y+1}}{{y-1}}}$, Solution is : $\left\{\vphantom{ x=\ln \left( \frac{y+1}{y-1}%
\right) }\right.$x = ln$\left(\vphantom{ \frac{y+1}{y-1}%
}\right.$${\frac{{y+1}}{{y-1}%
}}$$\left.\vphantom{ \frac{y+1}{y-1}%
}\right)$$\left.\vphantom{ x=\ln \left( \frac{y+1}{y-1}%
\right) }\right\}$ (Solve for x)

P = Qekt, Solution is : $\left\{\vphantom{ k=\frac{\ln \frac{P}{Q}}{t}}\right.$k = ${\frac{{\ln \frac{P}{Q}}}{{t}}}$$\left.\vphantom{ k=\frac{\ln \frac{P}{Q}}{t}}\right\}$ (Solve for k)

log$\left(\vphantom{ 3x+y}\right.$3x + y$\left.\vphantom{ 3x+y}\right)$ = 8, Solution is : $\left\{\vphantom{ x=\frac{1}{3}e^{8}-%
\frac{1}{3}y}\right.$x = ${\frac{{1}}{{3}}}$e8 - ${\frac{{1}}{{3}}}$y$\left.\vphantom{ x=\frac{1}{3}e^{8}-%
\frac{1}{3}y}\right\}$ (Solve for x)

log5$\left(\vphantom{ 4x^{2}-3y}\right.$4x2 - 3y$\left.\vphantom{ 4x^{2}-3y}\right)$ = 5$\scriptstyle {\frac{{5}}{{\ln 5}}}$, Solution is : $\left\{\vphantom{ x=-\frac{1}{2}\sqrt{\left( e^{5^{\frac{5}{\ln 5}}\ln 5}+3y\right) }%
}\right.$x = - ${\frac{{1}}{{2}}}$$\sqrt{{\left( e^{5^{\frac{5}{\ln 5}}\ln 5}+3y\right) }%
}$$\left.\vphantom{ x=-\frac{1}{2}\sqrt{\left( e^{5^{\frac{5}{\ln 5}}\ln 5}+3y\right) }%
}\right\}$,

                                $\left\{\vphantom{ x=\frac{1}{2}\sqrt{\left( e^{5^{\frac{5}{\ln 5}}\ln 5}+3y\right) }%
}\right.$x = ${\frac{{1}}{{2}}}$$\sqrt{{\left( e^{5^{\frac{5}{\ln 5}}\ln 5}+3y\right) }%
}$$\left.\vphantom{ x=\frac{1}{2}\sqrt{\left( e^{5^{\frac{5}{\ln 5}}\ln 5}+3y\right) }%
}\right\}$ (Solve for x)