11^x=18*10^(x+1)

11^x  =  18 * 10^(x + 1)                              Take the log of both sides to get:

log(11^x)  =  log(18 * 10^(x + 1)                   Use  log( A · B )  =  log(A) + log(B)  to get:

log(11^x)  =  log(18) + log( 10^(x + 1) )         Use  log( A ^ B )  =  B · log(A)  to get:

xlog(11)  =  log(18) + (x + 1)log(10)               Use  log(10)  =  1  to get:  

xlog(11)  =  log(18) + (x + 1)                           

xlog(11)  =  log(18) + x + 1

xlog(11) - x  =  log(18) + 1

x( log(11) - 1 )  =  log(18) + 1

x  =  [ log(18) + 1 ] / [ log(11) - 1 ] 

11^(x) = 18 * 10^(1) * 10^(x) ;

log( 11^(x) ) = log( 180) + log( 10^(x) ) ; because log(x*y) = log(x) * log(y)

xlog(11) = log(180) + xlog(10) ;

x[ log(11) - log(10) ] = log(180) ;

x = log(180) / [ log(11) - log(10) ] 

Sorry just a not. It is not log(x)*log(y) = log(x*y), but log(x*y) = log(x) + log(y).