Question

Resolva em r as seguintes equaçoes exponenciais

Answer 1

p)

$5^{2x^2+3x-2}=1\\\\5^{2x^2+3x-2}=5^0\\\\2x^2+3x-2=0\\\\x_1=1/2\\x_2=-2$

q)

$2^{8x-1}.2^8=8\\\\2^{8x-1+8}=2^3\\\\8x+7=3\\\\8x=-4\\\\x=-1/2$

r)

$3^{5x} /3^4=81\\\\3^{5x-4}=3^4\\\\5x-4=4\\\\5x=8\\\\x=8/5$

s)

$2^{3x-1}.4^{2x+3}=8^{3-x}\\\\2^{3x-1}.2^{2^{2x+3}}=2^{3^{3-x}}\\\\2^{3x-1}.2^{4x+6}=2^{9-3x}\\\\2^{3x-1+4x+6}=2^{9-3x}\\\\7x+5=9-3x\\\\10x=4\\\\x=2/5$

t)

$2^{3x+2}/8^{2x-7}=4^{x-1}\\\\2^{3x+2}/2^{3^{2x-7}}=2^{2^{x-1}}\\\\2^{3x+2}/2^{6x-21}=2^{2x-2}\\\\2^{3x+2-6x+21}=2^{2x-2}\\\\-3x+23=2x-2\\\\5x=25\\\\x=25/5\\\\x=5$