How to Solve Exponential & Logarithmic Equations

To solve an exponential or logarithmic equation, change the given equation into one of the following forms, where a and b are real numbers, a > 0 and

 a ≠ 1, and follow the guidelines.

1. $a^{f\left(x\right)}=b$
   Solve by taking the logarithm of both sides.
2. $\log_af\left(x\right)=b$
   Solve by changing to exponential form $a^b=f\left(x\right)$.
3. $\log_af\left(x\right)=\log_ag\left(x\right)$
   The given equation is equivalent to the equation $f\left(x\right)=g\left(x\right)$. Solve algebraically.
4. In a more complicated equation, it may be necessary to first solve for $a^{f\left(x\right)}$ or $\log_af\left(x\right)\:$and then solve the resulting equation using the methods above.
5. Check that each of the proposed solutions is in the domain.