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Question-179631




Question Number 179631 by daus last updated on 31/Oct/22
Commented by daus last updated on 31/Oct/22
solve for x
$${solve}\:{for}\:{x} \\ $$
Answered by Rasheed.Sindhi last updated on 31/Oct/22
64^(4x) =((1/4))^(3x)   4^(12x) .4^(3x) =1  4^(15x) =4^0   15x=0  x=0
$$\mathrm{64}^{\mathrm{4}{x}} =\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{3}{x}} \\ $$$$\mathrm{4}^{\mathrm{12}{x}} .\mathrm{4}^{\mathrm{3}{x}} =\mathrm{1} \\ $$$$\mathrm{4}^{\mathrm{15}{x}} =\mathrm{4}^{\mathrm{0}} \\ $$$$\mathrm{15}{x}=\mathrm{0} \\ $$$${x}=\mathrm{0} \\ $$
Commented by daus last updated on 31/Oct/22
thanks
$${thanks}\: \\ $$
Answered by Acem last updated on 01/Nov/22
64^(4x)  = 0.25^(3x)   12x ln 4= −3x ln 4  15x ln 4= 0 ⇒ x=0
$$\mathrm{64}^{\mathrm{4}{x}} \:=\:\mathrm{0}.\mathrm{25}^{\mathrm{3}{x}} \\ $$$$\mathrm{12}{x}\:\mathrm{ln}\:\mathrm{4}=\:−\mathrm{3}{x}\:\mathrm{ln}\:\mathrm{4} \\ $$$$\mathrm{15}{x}\:\mathrm{ln}\:\mathrm{4}=\:\mathrm{0}\:\Rightarrow\:{x}=\mathrm{0} \\ $$
Answered by Rasheed.Sindhi last updated on 01/Nov/22
64^(4x) =((1/4))^(3x) =4^(−3x) ={(4^3 )^(1/3) }^(−3x) =64^(−3x)    ⇒4x=−3x⇒12x=0⇒x=0
$$\mathrm{64}^{\mathrm{4}{x}} =\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{3}{x}} =\mathrm{4}^{−\mathrm{3}{x}} =\left\{\left(\mathrm{4}^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} \right\}^{−\mathrm{3}{x}} =\mathrm{64}^{−\mathrm{3}{x}} \\ $$$$\:\Rightarrow\mathrm{4}{x}=−\mathrm{3}{x}\Rightarrow\mathrm{12}{x}=\mathrm{0}\Rightarrow{x}=\mathrm{0} \\ $$

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