Question

Qual o conjunto solução de: Log10$\sqrt{x}$ + Log100ˣ = 2

Answer 1

vamos lá...

$\log_{10} \sqrt{x} +\log_{100}x=2 \\ \\ mudar~~\log_{100}x~~para~~base~~10 \\ \\ \log_{10} \sqrt{x} + \frac{\log_{10}x}{\log_{10}100} =2 \\ \\ \log_{10} \sqrt{x} + \frac{\log_{10}x}{2} =2 \\ \\ mmc=2 \\ \\ 2\log_{10} \sqrt{x} +\log_{10}x=4 \\ \\ \log_{10}( \sqrt{x} )^2+\log_{10}x=4 \\ \\ \log_{10}x+\log_{10}x=4 \\ \\ 2\log_{10}x=4 \\ \\ \log_{10}x=4\div2 \\ \\ \log_{10}x=2 \\ \\ x=10^2 \\ \\ x=100$