Question

Resolva as questoes
a) Logx 81 = 4/3
b) Log125 25= x

Answer 1

Resposta:

$\text{\sf Leia abaixo}$

Explicação passo-a-passo:

$\sf log_x\:81 = \dfrac{4}{3}$

$\sf x^{\frac{4}{3}} = 81$

$\sf x^{\frac{4}{3}} = 3^4$    

$\sf x = 3^k$

$\sf (3^k){\frac{4}{3}} = 3^4$    

$\sf \not3^{\frac{4k}{3}} = \not3^4$

$\sf \dfrac{4k}{3} = 4$

$\sf 4k = 12$

$\sf k = 3$

$\sf x = 3^3$

$\boxed{\boxed{\sf x = 27}}$

$\sf log_{125}\: 25 = x$

$\sf 125^x = 25$

$\sf \f(5.5^2)^x = 5^2$

$\sf 5^x.5^{2x} = 5^2$

$\sf \not5^{3x} = \not5^2$

$\sf 3x = 2$

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

Answer 2

Resolução da letra A:

⠀⠀$\sf log_x(81) = \dfrac{4}{3}$

⠀⠀$\sf x^{\left(\dfrac{4}{3}\right)} = 81$

⠀⠀$\sf {\left({x}^{\left(\dfrac{4}{3}\right)}\right)}^{\dfrac{3}{4}} = {81}^{\left(\dfrac{3}{4}\right)}$

⠀⠀$\sf {x}^{\left(\dfrac{4\cdot3}{3\cdot4}\right)} = {81}^{\left(\dfrac{3}{4}\right)}$

⠀⠀$\sf {x}^{\left(\dfrac{12}{12}\right)} = {({3}^{4})}^{\left(\dfrac{3}{4}\right)}$

⠀⠀$\sf x = {3}^{\left(\dfrac{4\cdot3}{4}\right)}$

⠀⠀$\sf x = {3}^{\left(\dfrac{12}{4}\right)}$

⠀⠀$\sf x = 3^3$

⠀⠀$\boxed{\textsf{ x} = \mathsf{27}}$

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Resolução da letra B:

⠀⠀$\sf log_{125}(25) =x$

⠀⠀$\sf 125^x = 25$

⠀⠀$\sf \left({{5}^{3}}\right)^{x} = 5^2$

⠀⠀$\sf 5^{3x} = 5^2$

⠀⠀$\sf3x=2$

⠀⠀$\boxed{\textsf{ x} =\mathsf{\dfrac{2}{3}}}$

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Espero Ter Ajudado !!