Questions: Solving exponential equations
Before attempting these questions, it is highly recommended that you read Guide: Solving exponential equations.
Solve each of the exponential equations below for the variable in the equation. If an equation has more than one variable, solve for the variable stated.
\(\quad\sqrt[4]{m-4}=5\)
\(\quad x^4=2^8\)
\(\quad 11^x=121^{(x-1)}\)
\(\quad y^{0.5}=23\)
\(\quad 8^{2-x}=2^{4+3x}\)
\(\quad 2^{3x}=10\)
\(\quad 5^{3-a}=625\)
\(\quad 16^{2x}=4^{x-1}\)
\(\quad 7^{2-x}=4^{2x+3}\)
\(\quad 16=8^{3-7x}\)
\(\quad e^{3-8p}-9=0\)
\(\quad e^{4-3q}+8=12\)
\(\quad \sqrt[3]{2^{4l}-4}=5\)
\(\quad \sqrt[3]{e^{2h}-13}=81^{\frac{1}{4}}\)
\(\quad \dfrac{5xa^{-7}b^{9}}{9a^2b^{-10}} = \dfrac{25b^{19}}{3a^9}\), solve for \(x\).
\(\quad 4^x\cdot 2^x=64\)
\(\quad {\dfrac{5^{x+1}\cdot6^{x+1}}{3^{x+1}}}=100\)
\(\quad \dfrac{\left[\left(\frac{1}{2}\right)^x\cdot\left(\frac{-1}{4}\right)^x\right]}{\left(\frac{2}{3}\right)^x}=-\dfrac{27}{4096}\)
\(\quad 3^{b+1}=7^b\)
\(\quad 5^{x+1}+5^x=12\)
\(\quad 2^{3z-1}=10^z\)
\(\quad 2^{2v}-2^{v+3}-2^4=0\)
After attempting the questions above, please click this link to find the answers.
Version history and licensing
v1.0: initial version created 08/23 by Zoë Gemmell, Isabella Lewis, Akshat Srivastava as part of a University of St Andrews STEP project.
- v1.1: edited 05/24 by tdhc.