3log_8(512^{x^{2}})=36 Find x

3log_8(512^{x^{2}})=36 Find x

Question
Logarithms
asked 2021-02-12
\(3\log_8(512^{x^{2}})=36\)
Find x

Answers (1)

2021-02-13
Divide both sides by 3
\(\log_8(512^{x^{2}})=12\)
Write in expinential form: \(\log_b a=x\to b^{x}=a\)
\(8^{1} 2=512^{x}\)
Since \(8^{3}=512\), we can write
\(8^{1} 2=(8^{3})^(x^{2})\)
\(8^{1} 2=8^{3x^{2}}\)
Equate exponens
\(12=3x^{2}\)
\(4=x^{2}\)
x=2 x= -2
0

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