Question

Find positive no. x which satisfy the equation ` log_3 x * log_4 x (log_5 x -1) = log_5 x*(log_4 x+ log_3 x)`

Answer 1

`log_3^xlog_4^x(log_5^x-1)=log_5^x(log_4^x+log_3^x)`
`log_3^xlog_4^xlog_5^x-log_3^xlog_4^x=log_5^xlog_4^x+log_5^xlog_3^x`
divide by`log_3^xlog_4^xlog_5^x`
`1=1/log_5^x+1/log_3^x+1/log_4^x`
`1=log_x^(5*4*3)`
`1=log_x^60`
`x=60,1`.