Помогите решить! [tex] 12^x*18^x=6^(x+6) [/tex]. Created by danilaborziy. algebra-ru

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Помогите решить!

[tex] 12^x*18^x=6^(x+6) [/tex]

snow99

$12^{x}*18^x} =6^{x+6}\\\\\frac{12^{x}*18^{x}}{6^{x}}=\frac{6^{x+6}}{6^{x}},6^{x} \neq0 \\\\2^{x}*18^{x} =6^{6}\\\\36^{x}=6^{6}\\\\6^{2x}=6^{6}\\\\2x=6\\\\x=3$

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Universalka

Verified answer

${12}^{x} \times {18}^{x} = {6}^{x + 6} \\ {2}^{x} \times {6}^{x} \times {3}^{x} \times {6}^{x} = {6}^{x + 6} \\ {6}^{x} \times {6}^{x} \times {6}^{x} = {6}^{x + 6} \\ {6}^{3x} = {6}^{x + 6} \\ 3x = x + 6 \\ 3x - x = 6 \\ 2x = 6 \\ x = 3$
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