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Exponents and Radicals: Difficult Problems with Solutions

Problem 1
What is the value of $x$ if
$2^{x+1}+2^{x}+2^{x-1}=28$
Problem 2
What is the value of $x$ if
$4^{\sqrt{x+1}}-2^{\sqrt{x+1}+2}=0$
Problem 3
What is the value of $x$ if $5^{3x}-5^{3x+1}+5^{3x+2}=3 \cdot 7\cdot 25^{3}$
Problem 4
What is the value of $x$ if
$3^{1-x}-3^{x}=2$
Problem 5
What is the value of $x$ if
$2-3^{-x}+3^{x+1}=0$
Problem 6
What is the value of x?
$56^{2x-8}=1$
Problem 7
What is the value of x?
$3^{7-2x}=(\frac{1}{27})^{-8}$
Problem 8
What is the value of x?
$\left(\frac{9}{8}\right)^{3x+12}=1$
Problem 9
What is the value of x?
$3^{7x+4}=\left(\frac{1}{27}\right)^{x-3}$
Problem 10
What is the value of x?
$2^{8x-4}\cdot 16^{3x-5}=16^{9x+2}$

Problem 11
What is the value of x?
$\left(\frac{1}{64}\right)^{-8x+3}=\left(\frac{1}{16}\right)^{7x-2}$
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