`x+log_10(2^x+1)=xlog_10 5+log_10 6`
`log_10 10^x=xlog_10 10=lambda`
`log_10 10^lambda+log_10(2^lambda+1)=log_10 5^x+log_10 6`
`2^x*5^x[2^x+1]=6*5^x=5^lambda[2^(2lambda(+2^lambda-6))]=0`
`5^x=0,2^(2lambda)+2^lambda-6=0`
`2^x=t^2+t-6=0`
`t^2+3t-2t-6=0`
`t(t+30-2(t+3)=0`
`(t-2)(t+3)=0`
`t=2,-3`
`2^lambda-2=0`
`lambda=1`.
