Question

Determine o valor de x em cada logaritmo



A) a) log2 64 = x


B) log5 625 = x


C) Log3 243 = x



D) Log3 9 = x


E) Log5 625 = x


F) Log16 2 =



G) Log8 64 = x



H) Log625 125 = x



I) Log256 64 = x



J) log729 27 =

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{a)\:log_2\:64 = x \iff 2^x = 64 \iff 2^x = 2^6 \iff x = 6}$

$\mathsf{b)\:log_5\:625 = x \iff 5^x = 625 \iff 5^x = 5^4 \iff x = 4}$

$\mathsf{c)\:log_3\:243 = x \iff 3^x = 243 \iff 3^x = 3^5 \iff x = 5}$

$\mathsf{d)\:log_3\:9 = x \iff 3^x = 9 \iff 3^x = 3^2 \iff x = 2}$

$\mathsf{e)\:log_5\:625 = x \iff 5^x = 625 \iff 5^x = 5^4 \iff x = 4}$

$\mathsf{f)\:log_{16}\:2 = x \iff (16)^x = 2 \iff 2^{4x} = 2^1 \iff x = \dfrac{1}{4}}$

$\mathsf{g)\:log_{8}\:64 = x \iff 8^x = 64 \iff 8^x = 8^2 \iff x = 2}$

$\mathsf{h)\:log_{625}\:125 = x \iff (625)^x = 125 \iff 5^{4x} = 5^3 \iff x = \dfrac{3}{4}}$

$\mathsf{i)\:log_{256}\:64 = x \iff (256)^x = 64 \iff 2^{8x} = 2^6 \iff x = \dfrac{3}{4}}$

$\mathsf{j)\:log_{729}\:27 = x \iff (729)^x = 27 \iff 3^{6x} = 3^3 \iff x = \dfrac{1}{2}}$