Question

(2^x+1) / (2^x-1) = 5, kindly solve this.its about logarithms, thanks

Answer 1

$\frac{ {2}^{x} + 1 }{ {2}^{x} - 1 } = 5 \\ {2}^{x} + 1 = 5 \times {2}^{x} - 5 \\ 4 \times {2}^{x} = 6 \\ {2}^{x + 1} = 3 \\ taking \: log_{e} \: on \: both \: sides \\ (x + 1) log_{e}2 = log_{e}3 \\ x = \frac{ log_{e}3 - log_{e}2 }{ log_{e}2 } \\ x = \frac{ log_{e} \frac{3}{2} }{ log_{e}2 } \\ x = log_{2} \frac{3}{2}$
hope it helps