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log-x-1-2-64-3-What-is-x-




Question Number 35897 by imamu222 last updated on 25/May/18
log_x^(1/2 )  64=3. What is x?
$${log}_{{x}^{\mathrm{1}/\mathrm{2}\:} } \mathrm{64}=\mathrm{3}.\:{What}\:{is}\:{x}? \\ $$
Commented by Cheyboy last updated on 25/May/18
log_x^(1/2)  64=3  64=(x^(1/2) )^3   64=x^(3/2)   (2)^6 =x^(3/2)   (2)^(6×2/3) =x  2^4 =x  x=16
$${log}_{{x}^{\mathrm{1}/\mathrm{2}} } \mathrm{64}=\mathrm{3} \\ $$$$\mathrm{64}=\left({x}^{\mathrm{1}/\mathrm{2}} \right)^{\mathrm{3}} \\ $$$$\mathrm{64}={x}^{\mathrm{3}/\mathrm{2}} \\ $$$$\left(\mathrm{2}\right)^{\mathrm{6}} ={x}^{\mathrm{3}/\mathrm{2}} \\ $$$$\left(\mathrm{2}\right)^{\mathrm{6}×\mathrm{2}/\mathrm{3}} ={x} \\ $$$$\mathrm{2}^{\mathrm{4}} ={x} \\ $$$${x}=\mathrm{16} \\ $$
Commented by imamu222 last updated on 25/May/18
Thanks a lot
$${Thanks}\:{a}\:{lot} \\ $$

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