Question

Sabendo que 10^1,079=12,qual o valor de x que satisfaz a equação 12^x=100.
(log100 na base 12=x)

Answer 1

log 12 = 1,079

log(12)100 = log 100/log 12 = 2/1,079 = 1,85

Answer 2

$12^x=100~~~~~~~~~~~~~~e~~~~~~10^{1,079}=12\\ \log_{12}(100)=x~~~~~~~~~~~~~~~\log_{10}(12)=1,079\\\\ passemos~para~a~base~dos ~logaritmos~dados..\\\\ \log_{12}(100)=x\\\\ x= \dfrac{\log(100)}{\log(12)}\\\\\\ x= \dfrac{\log_{10} (10)^2}{\log_{10}(12)}\\\\\\ x= \dfrac{2\cdot\log_{10}(10)}{\log_{10}(12)}\\\\\\ \log_{10}(10)=1~~e~~\log_{10}(12)=1,079\\\\\\ x= \dfrac{2\cdot1}{1,079}\\\\\\ x= \dfrac{2}{1,079}\\\\\\ \Large\boxed{x\approx1,853}$