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Question Number 16823 by tawa tawa last updated on 26/Jun/17

solve for g.  6(4^x  + g^x ) = 13.6^x

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{g}. \\ $$$$\mathrm{6}\left(\mathrm{4}^{\mathrm{x}} \:+\:\mathrm{g}^{\mathrm{x}} \right)\:=\:\mathrm{13}.\mathrm{6}^{\mathrm{x}} \\ $$

Commented by mrW1 last updated on 26/Jun/17

x≠0  4^x +g^x =13×6^(x−1)   g^x =13×6^(x−1) −4^x   g=(13×6^(x−1) −4^x )^(1/x)

$$\mathrm{x}\neq\mathrm{0} \\ $$$$\mathrm{4}^{\mathrm{x}} +\mathrm{g}^{\mathrm{x}} =\mathrm{13}×\mathrm{6}^{\mathrm{x}−\mathrm{1}} \\ $$$$\mathrm{g}^{\mathrm{x}} =\mathrm{13}×\mathrm{6}^{\mathrm{x}−\mathrm{1}} −\mathrm{4}^{\mathrm{x}} \\ $$$$\mathrm{g}=\left(\mathrm{13}×\mathrm{6}^{\mathrm{x}−\mathrm{1}} −\mathrm{4}^{\mathrm{x}} \right)^{\mathrm{1}/\mathrm{x}} \\ $$

Commented by tawa tawa last updated on 26/Jun/17

God bless you sir.   i have recheck,  it is  9^x   and  (13.6) is a decimal point.  (13.6)^x

$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\: \\ $$$$\mathrm{i}\:\mathrm{have}\:\mathrm{recheck},\:\:\mathrm{it}\:\mathrm{is}\:\:\mathrm{9}^{\mathrm{x}} \:\:\mathrm{and}\:\:\left(\mathrm{13}.\mathrm{6}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{decimal}\:\mathrm{point}.\:\:\left(\mathrm{13}.\mathrm{6}\right)^{\mathrm{x}} \\ $$

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