Question

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Answer 1

$a) 25^{x}=125 \\ 5^{2x}=5^{3} \\2x=3 \\x=\frac{3}{2} \\ b) (\frac{1}{2})^{x}=4\\2^{-x}=2^{2} \\ x=-2 \\ c)8^{x}.8^{4}=64 \\8^{x+4}=8^{2} \\ x+4 =2 \\ x=-2 \\ d)9^{2x}.9=81^{4} \\9^{2x+1}=9^{8} \\2x+1=8 \\ x=\frac{7}{2}\\e)49^{x^{2}}.343=7^{2} \\ 7^{2x^{2}}=7^{2}.7^{3} \\2 x^{2} =5 \\ x=+/- \sqrt{ \frac{5}{2}} \\f) 4^{ x^{2}-16}=1 \\ x^{2}-16=0 \\ x=+/- \sqrt{16} \\ x=+/-4 \\ g)10^{ x^{2}+4x+4}=1 \\ x^{2}+4x+4=0 \\ (x+2)^{2}=0 \\ x+2=0 \\ x=-2$