Question

1º) Resolva as equações exponenciais:

A) $3^{X}$ = $\sqrt[5]{27}$

B) $4^{X}$ = $\sqrt[]{32}$

C) $25^{2X}$ = $\sqrt[]{5}$

Answer 1

Resposta:

A)

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

B)

${4}^{x} = \sqrt{32} \\ { ({2}^{2}) }^{x} = {32}^{ \frac{1}{2} } \\ {2}^{2x} = {( {2}^{5} )}^{ \frac{1}{2} } \\ {2}^{2x} = {2}^{ \frac{5}{2} } \\ 2x = \frac{5}{2} \\ x = \frac{ \frac{5}{2} }{2} = \frac{5}{2} \times \frac{1}{2} = \frac{5}{4}$

C)

${25}^{2x} = \sqrt{5} \\ {( {5}^{2}) }^{2x} = {5}^{ \frac{1}{2} } \\ {5}^{4x} = {5}^{ \frac{1}{2} } \\ 4x = \frac{1}{2} \\ x = \frac{ \frac{1}{2} }{4} = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$

Explicação passo-a-passo:

Espero ter ajudado.