Question

a) Log0,25 8 = x b) Log25 0,008 = x c) Log0,01 0,001 = x

Answer 1

Explicação passo-a-passo:

a)

$\sf log_{0,25}~8=x$

$\sf (0,25)^x=8$

$\sf \Big(\dfrac{1}{4}\Big)^x=2^3$

$\sf (2^{-2})^{x}=2^3$

$\sf 2^{-2x}=2^3$

Igualando os expoentes:

$\sf -2x=3$

$\sf 2x=-3$

$\sf \red{x=\dfrac{-3}{2}}$

b)

$\sf log_{25}~0,008=x$

$\sf 25^x=0,008$

$\sf (5^2)^x=\dfrac{8}{1000}$

$\sf 5^{2x}=\dfrac{1}{125}$

$\sf 5^{2x}=5^{-3}$

Igualando os expoentes:

$\sf 2x=-3$

$\sf \red{x=\dfrac{-3}{2}}$

c)

$\sf log_{0,01}~0,001=x$

$\sf (0,01)^x=0,001$

$\sf (10^{-2})^x=10^{-3}$

$\sf 10^{-2x}=10^{-3}$

Igualando os expoentes:

$\sf -2x=-3$

$\sf 2x=3$

$\sf \red{x=\dfrac{3}{2}}$