Respuesta :

[tex]\\ \rm\Rrightarrow 49(7^{3x-8})=343^{4x+9}[/tex]

[tex]\\ \rm\Rrightarrow 7^2(7^{3x-8})=(7^3)^{4x+9}[/tex]

[tex]\\ \rm\Rrightarrow 7^{2+3x-8}=7^{3(4x+9)}[/tex]

[tex]\\ \rm\Rrightarrow 7^{3x-6}=7^{12x+27}[/tex]

[tex]\\ \rm\Rrightarrow 3x-6=12x+27[/tex]

[tex]\\ \rm\Rrightarrow -33={9x}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{-33}{9}[/tex]

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[tex] x = - \frac{33}{9} [/tex]

Step-by-step explanation:

[tex](49)(7 {}^{3x - 8} ) = 343 {}^{4x + 9} [/tex]

As we know 7² = 49 and 7³= 343

[tex]7 {}^{2} (7 {}^{3x - 8} ) = (7 {}^{3} ) {}^{4x + 9} [/tex]

Taking 7 as common

[tex]7 {}^{3x - 6} = 7 {}^{12x + 27} [/tex]

[tex]3x - 6 = 12x + 27[/tex]

Taking like terms one side .

[tex]3x - 12x = 27 + 6[/tex]

[tex] - 9 x = 33[/tex]

[tex]x = - \frac{33}{9} [/tex]

[tex]\sf\red{hope\:it\:helps\:you}[/tex]

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