Exponential Equations: Problems with Solutions

By Denitsa Dimitrova (Bulgaria)
Problem 1
$3^{2x+1}=27$
Problem 2
$\sqrt[3]{2^x}=128$
Problem 3
$\left(\frac{1}{3}\right)^{x^2-4x+4.5}=\sqrt{\frac{1}{3}}$
Problem 4
$\left(\frac56\right)^x=\left(\frac{36}{25}\right)^2$
Problem 5
$\left(\frac{1}{2}\right)^{\frac{x-1}{x+2}}=4$
Problem 6
$\sqrt[3]{8^{x+2}}=\sqrt{4^{3x-2}}$
Problem 7
$6^{x^2+5}=\frac{1}{64^x\cdot3^{6x}}$
Problem 8
$9+9^x=10\cdot 3^x$
Problem 9
$9^x+2\cdot3^x-15=0$
Problem 10
$3\cdot25^x-2\cdot5^x-1=0$

Problem 11
$2\cdot3^{3x-1}+27^{x-\frac{2}{3}}=9^{x-1}+2\cdot3^{2x-1}$
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