Question

Hola me podrian ayudar?

Answer 1

Respuesta:

a) x=3

b) x=3

Explicación paso a paso:

lo terminaré más rato

Answer 2

Explicación paso a paso:

a.

$log_{10}(1000) \\ {10}^{x} = 1000 \\ {10}^{x} = {10}^{3} \\ x = 3$

b.

$log_{3}(81) = x \\ {3}^{x} = 81 \\ {3}^{x} = {3}^{4} \\ x = 4$

c.

$log_{2}( \frac{1}{4} ) = x \\ {2}^{x} = \frac{1}{4} \\ {2}^{x} = {2}^{ - 2} \\ x = - 2$

d.

$log_{ \frac{1}{3} }( \frac{1}{81} ) = x \\ { \frac{1}{3} }^{x} = { \frac{1}{3} }^{4} \\ {3}^{ - x} = {3}^{ - 4} \\ - x = - 4 \\ x = 4$

e.

$log_{x}(9) = 2 \\ {x}^{2} = 9 \\ {x}^{2} = {3}^{2} \\ x = 3$

f.

$log_{x}( \frac{1}{25} ) = - 2 \\ {x}^{ - 2} \frac{1}{25} \\ {x}^{ - 2} = { \frac{1}{5} }^{2} \\ {x}^{ - 2} = {5}^{2} \\ x = 5$

g.

$log_{x}(16) = - 4 \\ \frac{1}{ log_{16}(x) } = - 4 \\ 1 = - 4 log_{16}(x) \\ - \frac{1}{4} = log_{16}(x) \\ x = {16}^{ - \frac{1}{4} } \\ x = \frac{1}{2}$

h.

$log_{2}(x) = 3 \\ {2}^{3} = x \\ 8 = x$

i.

$log_{27}( \frac{x}{5} ) = \frac{1}{3} \\ {27}^{ \frac{1}{3} } = \frac{x}{5} \\ \sqrt[3]{27} = \frac{x}{5} \\ 3 = \frac{x}{5} \\ x = 15$

j.

$log_{2}(x + 1) = 0 \\ {2}^{0} = x + 1 \\ 1 = x + 1 \\ 1 - 1 = x \\ 0 = x$

k.

$log_{3}(8x + 9) = 4 \\ {3}^{4} = 8x + 9 \\ 81 = 8x + 9 \\ 81 - 9 = 8x \\ \frac{72}{8} = 9 \\ 9 = x$