Question

Se log na base b de 100 = 4, então o logaritmo decimal de b é?

Answer 1

log 100=4 >>>>> b^(4)=100
b

>>>>>>> b=
$\sqrt[4]{100}$
que dará
${10}^{0.5}$

Answer 2

$\log_{b}{100} = 4 \iff {b}^{4} = 100 \\ {b}^{4} = {10}^{2} \Rightarrow { ({b}^{4}) }^{ \frac{1}{4} } = { ({10}^{2}) }^{ \frac{1}{4} } \\ b = {10}^{ \frac{1}{2} } \Rightarrow \log{b} = \frac{1}{2} \\ \boxed{ \log{b} = 0,5 } \\ \\ ou \\ \\ \log_{b}{100} = 4 \Rightarrow \frac{ \log{100} }{ \log{b} } = 4 \\ \frac{ \log{ {10}^{2} }}{4} = \log{b} \Rightarrow \log{b} = \frac{ 2 \cdot \log{10} }{4} \\ \log{b} = \frac{2 \cdot 1}{4} = \frac{1}{2} \\ \boxed{\log{b} = 0,5}$