Question

64^(x-1) = 8^(x+6)
27^x = 3^x-12
7^x = 1/49
2^x = 1/128
5^x = 625

Answer 1

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1)

$\tt{a)}~\sf{64^{x-1}=8^{x+6}}\\\sf{(8^2)^{x-1}=8^{x+6}}\\\sf{8^{2x-2}=8^{x+6}$

$\sf{2x-2=x+6}\\\sf{2x-x=6+2}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{x=8}}}}}$

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2)

$\sf{27^x=3^{x-12}}\\\sf{(3^3)^x=3^{x-12}}\\\sf{3^{3x}=3^{x-12}}\\\sf{3x=x-12}\\\sf{3x-x=12}\\\sf{2x=12}\\\sf{x=\dfrac{12}{2}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{x=6}}}}}$

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3)

$\sf{7^x=\dfrac{1}{49}}\\\sf{7^x=7^{-2}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{x=-2}}}}}$

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4)

$\sf{2^x=\dfrac{1}{128}}\\\sf{2^x=2^{-7}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{x=-7}}}}}$

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5)

$\sf{5^x=625}\\\sf{5^x=5^4}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{x=4}}}}}$

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