We have to find the exact solution to the equation.
We can solve it as:
[tex]\begin{gathered} 10^{1-x}=6^x \\ (1-x)\cdot\ln10=x\cdot\ln(6) \\ \ln10-\ln10\cdot x=\ln6\cdot x \\ \ln10=(\ln6-\ln10)x \\ x=\frac{\ln10}{\ln6-\ln10} \end{gathered}[/tex]
b) If we use a calculator to find the logarithms we obtain the approximate value of x as:
[tex]\begin{gathered} \ln10\approx2.3025851 \\ \ln6\approx1.7917595 \\ \Rightarrow x\approx\frac{2.3025851}{1.7917595-2.3025851}=\frac{2.3025851}{-0.5108256}\approx-4.507576 \end{gathered}[/tex]
Answer:
a) x = ln(10)/(ln(6)-ln(10))
b) x = -4.507576
