Question 185437
*[Tex \LARGE \log_{4}\left(1024\right)=x] ... Start with the given equation.



*[Tex \LARGE 1024=4^{x}] ... Rewrite the equation using the property *[Tex \LARGE \log_{b}\left(x\right)=b^y=x\Leftrightarrow y]



*[Tex \LARGE 1024=\left(2^{2}\right)^{x}] ... Rewrite {{{4}}} as {{{2^2}}}



*[Tex \LARGE 2^{10}=\left(2^{2}\right)^{x}] ... Rewrite {{{1024}}} as {{{2^10}}}



*[Tex \LARGE 2^{10}=2^{2x}] ... Multiply the exponents.



*[Tex \LARGE 10=2x] ... Since the bases are equal, the exponents are equal.



*[Tex \LARGE \frac{10}{2}=x] ... Divide both sides by 2 to isolate "x".



*[Tex \LARGE 5=x] ... Divide



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Answer:



So the solution is *[Tex \LARGE x=5]