Question

Rezolvati in R ecuatia 3 la puterea x la a 2 a -1 = 3

Answer 1

Nu prea am inteles ce ai vrut sa spui. O sa presupun ca asta ai vrut sa scrii:

$(3^{x})^{2}-1=3\\3^{x}=u\\u^{2}-1=3\\u^{2}-1+1=3+1\\u^{2} =4\\u=\pm\sqrt{4\\}  3^{x}=\pm \sqrt{4}\\3^{x}=- \sqrt{4}\Rightarrow x\notin\mathds{R}\\3^{x}= \sqrt{4}\Rightarrow ln(3^{x})=ln\sqrt{4}\\ \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\hspace (formula)\\\ln \left(3^x\right)=x\ln \left(3\right),\:\space\ln \left(\sqrt{4}\right)=\frac{1}{2}\ln \left(4\right)\\x\ln \left(3\right)=\frac{1}{2}\ln \left(4\right)\\\frac{1}{2}\ln \left(4\right)=2\cdot \frac{1}{2}\ln \left(2\right)$

$=\ln \left(2\right)\\x\ln \left(3\right)=\ln \left(2\right)\\x=\frac{\ln \left(2\right)}{\ln \left(3\right)}$