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

Question
Logarithms
$$3\log_8(512^{x^{2}})=36$$
Find x

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

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