Question

6^(x/2)=3^(1-x)

Answer 1

i need help solving it using logs!!!

Answer 2

\[6^{\left(\frac{x}{2}\right)} = 3^{(1-x)}\]\[\sqrt[2]{6^x} = 3^1 \dot\ 3^{-x}\]\[\sqrt[2]{6^x} = \frac{3^1}{3^{x}}\] Square both sides to get: \[6^x = \left(\frac{3^1}{3^{x}}\right)^2\] \[6^x = \frac{3^2}{3^{2x}}\] \[6^x = \frac{3^2}{9^{x}}\]
\[6^x \dot\ 9^x = 3^2\]\[6^x \dot\ 9^x = 9\]\[(6 \dot\ 9)^x = 9\]\[(54)^x = 9\]

From there take logs to get

\[x \log(54) = \log(9)\]

Divide both sides by log(54) to get

\[x = \frac{\log(9)}{\log(54)}\]