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Solve-100-x-200-




Question Number 199486 by hardmath last updated on 04/Nov/23
Solve:   100^x  = 200
$$\mathrm{Solve}:\:\:\:\mathrm{100}^{\boldsymbol{\mathrm{x}}} \:=\:\mathrm{200} \\ $$
Answered by cortano12 last updated on 04/Nov/23
log _(10) (100^x )= log _(10) (200)    2x = 2+log _(10) (2)     x=1+log _(10) ((√2) )
$$\mathrm{log}\:_{\mathrm{10}} \left(\mathrm{100}^{\mathrm{x}} \right)=\:\mathrm{log}\:_{\mathrm{10}} \left(\mathrm{200}\right) \\ $$$$\:\:\mathrm{2x}\:=\:\mathrm{2}+\mathrm{log}\:_{\mathrm{10}} \left(\mathrm{2}\right) \\ $$$$\:\:\:\mathrm{x}=\mathrm{1}+\mathrm{log}\:_{\mathrm{10}} \left(\sqrt{\mathrm{2}}\:\right) \\ $$
Answered by Skabetix last updated on 04/Nov/23
xln(100)=ln(200)  x=((ln(200))/(ln(100)))=((log(200))/2)
$${xln}\left(\mathrm{100}\right)={ln}\left(\mathrm{200}\right) \\ $$$${x}=\frac{{ln}\left(\mathrm{200}\right)}{{ln}\left(\mathrm{100}\right)}=\frac{{log}\left(\mathrm{200}\right)}{\mathrm{2}} \\ $$

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