Question

(AJUDA) Equação Exponencial

A) 64^3x-1=8

B) 8^3x+4.4^2x-1=16x+1

Answer 1

a )

$64^{3x-1}=8\\ \\(2^6)^{3x-1}=2^3\\ \\\not{2}^{18x-6}=\not{2}^3\\ \\18x-6=3\\ \\18x=9\\ \\x= \frac{9}{18} \\ \\\boxed{\therefore~x= \frac{1}{2} }$

b )

$8^{3x+4}*4^{2x-1}=16^{x+1}\\ \\(2^3)^{3x+4}*(2^2)^{2x-1}=(2^4)^{x+1} \\ \\2^{9x+12}*2^{4x-2}=2^{4x+4}\\ \\2^{9x+12+4x-2}=2^{4x+4}\\ \\\not{2}^{13x+10}=\not{2}^{4x+4}\\ \\13x+10=4x+4\\ \\9x=-6\\ \\\boxed{\therefore~x= -\frac{2}{3} }$