Respuesta :

Given the equation;

[tex]32^{x-1}=16^{x+4}[/tex]

We express 32 and 16 as an index of 2, we have;

[tex](2^5)^{x-1}=(2^4)^{x+4}^{}[/tex]

Then, we multiply the exponents, we have;

[tex]2^{5x-5}=2^{4x+16}[/tex]

So, we take out the 2 from both sides, we have;

[tex]\begin{gathered} 5x-5=4x+16 \\ \end{gathered}[/tex]

Then, we collect like terms, we have;

[tex]\begin{gathered} 5x-4x=16+5 \\ x=21 \end{gathered}[/tex]

CORRECT OPTION: 21

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