Find \(log_23\cdot log_34...log_(127)128\)

By the way, the (127) was supposed to be the bottom number, but the latex wouldn't allow more than one digit.

You needed to put the 127 in parenthesis, not brackets, they are the curly ones {127 }

\(log_23\cdot log_34...log_{127}128\\ =\frac{log3}{log2}\cdot \frac{log4}{log3}\dots \cdot \frac{log128}{log127}\\ cancel\\ =\frac{log128}{log2}\\ =\frac{log2^7}{log2}\\ =\frac{7log2}{log2}\\ =7\)

thank you!