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`ln40+2ln(1/2)+lnx` Condense the expression.

`ln40+2ln(1/2) + lnx`


First, apply the logarithm rule `log_b (a^m)=m*log_b(a)` .


`= ln40 + ln(1/2)^2 + ln x`


`=ln40+ ln(1/4) + lnx`


And, apply the rule `log_b(m*n) = log_bm +log_b n` .


`= ln (40 * 1/4*x)`


`=ln (10x)`


Therefore,  `ln40+2ln(1/2) + lnx=ln(10x)` .

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