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Homework Statement
This is re-asking the question in https://www.physicsforums.com/showthread.php?t=273275" which mysteriously went quiet before the answer could be given... Anyway I also tried answering the question, but to no avail.
Homework Equations
[tex]a^m.a^n=a^{m+n}[/tex]
[tex](a^m)^n=a^{mn}[/tex]
[tex]log(ab)=loga+logb[/tex]
[tex]log(a^b)=bloga[/tex]
The Attempt at a Solution
[tex]12^x=4.8^{2x}[/tex]
[tex]3^x.(2^2)^x=2^2(2^3)^{2x}[/tex]
[tex]3^x.2^{2x}-2^{6x+2}=0[/tex]
[tex]2^{2x}(3^x-2^{4x-2})=0[/tex]
Hence, [tex]2^{2x}=0[/tex] (1) or [tex]3^x-2^{4x-2}=0[/tex] (2)
(1) has no solution.
(2) [tex]\Rightarrow[/tex] [tex]3^x=2^{4x+2}[/tex]
[tex]xlog3=(4x+2)log2[/tex]
How can one go about solving this? different bases? It gives an answer of [tex]x\approx -0.82814[/tex]
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