Help! Need answers in two days max!

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

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

thank you!