Use logarithms to solve the equation 7^{x}=2^{x+1}, giving the value of x correct to 3 significant figures.

Answer:

7^{x}=2^{x+1}

Using logarithm on both sides, we get 

\log 7^{x}=\log 2^{x+1}  \\ \\  \therefore x\log 7=\left( x+1\right) \log 2  \\ \\  x\log 7=x\log 2+\log 2  \\ \\  x\log 7-x\log 2=\log 2  \\ \\  x\left( \log 7-\log 2\right) =\log 2  \\ \\  x=\dfrac {\log 2}{\log 7-\log 2}  \\ \\  x=0.553

Advertisements