Question

PRECISO DE AJUDA COM ESSAS QUESTÕES DE LOG URGENTE

Answer 1

1)

a)

$\log_2{256}=x\iff 2^x=256\ \to\ 2^x=2^8\ \to\ \boxed{x=8}$

b)

$\log_7{\dfrac{1}{49}}=x\ \to\ 7^x=\dfrac{1}{49}\ \to\ 7^x=7^{-2}\ \to\ \boxed{x=-2}$

c)

$\log{x}=4\ \to\ 10^4=x\ \to\ \boxed{x=10000}$

2)

$\log_2{125}=\log_2{5^3}=3\log_2{5}\approx3(2.32)\approx\boxed{6.96}$

3)

a)

$\log_5{5}=\dfrac{\ln{5}}{\ln{5}}=\boxed{1}$

b)

$\log_2{1}=\dfrac{\ln{1}}{\ln{2}}=\boxed{0}$

c)

$\log_3{3^4}=4\log_3{3}=4\dfrac{\ln{3}}{\ln{3}}=\boxed{4}$

d)

$2^{\log_2{8}}=2^3=\boxed{8}$

4)

a)

$\log_{6}{16}=\log_6{2^4}=4\log_6{2}\approx4(0.39)\approx\boxed{1.56}$

b)

$\log_6{22}=\log_6{(2\times11)}=\log_6{2}+\log_6{11}\approx0.39+1.34\approx\boxed{1.73}$

c)

$\log_6{44}=\log_6{(2^2\times11)}=2\log_6{2}+\log_6{11}\approx2(0.39)+1.34\approx\boxed{2.12}$