Question

Equação exponencial
A) ^5√100. 10^x= 0,1
B) 16^x /2^2x+3= 256

Me ajudem, por favor

Answer 1

Explicação passo-a-passo:

$A)\\ \sqrt[5]{100} .10^x=0,1\\ \\ \sqrt[5]{10^2} .10^x=10^{-1}\\ \\ 10^{{2\over5}}.10^x=10^{-1}\\ \\ 10^{{2\over5}+x}=10^{-1}\\ \\ {2\over5}+x=-1\\ \\ 2+5x=-5\\ \\ 5x=-5-2\\ \\ 5x=-7\\ \\ x=-{5\over7}$

$B)\\ {16^x\over2^{2x+3}}=256\\ \\ {2^{4x}\over2^{2x+3}}=2^8\\ \\ 2^{4x}=2^8.2^{2x+3}\\ \\ 2^{4x}=2^{8+2x+3}\\ \\ 2^{4x}=2^{11+2x}\\ \\ 4x=11+2x\\ \\ 4x-2x=11\\ \\ 2x=11\\ \\ x={11\over2}$

Answer 2

Resposta:

$\sqrt[5]{100} .10 ^{x} = 0.1 \\ \sqrt[5]{10 ^{2} } .10^{x} = 10 ^{ - 1} \\ 10 ^{ \frac{2}{5} } .10^{x} = 10 ^{ - 1} \\ 10^{ \frac{2}{5} - x } = 10 ^{ - 1} \\ \frac{2}{5} + x = - 1 \\ 2 + 5x = - 5 \\ 5x = - 5 - 2 \\ 5x = - 7 \\ x = - \frac{7}{5}$

2)

B) 16^x /2^2x+3= 256