How do i simplify (log_2 3)(log_3 4)(log_4 5)

its the change of base law?
but i dont really get how to use it :(

log_2 3 = log 3/ log 2
log_3 4 = log 4/log 3
log_4 5 = log 5/log 4

(log 3/log 2)*(log 4/ log 3)*(log 5/ log 4) = log 5/log 2 ....everything is log base 10 now

If you have log of x to the base a this is the same as log x to the base b divided by log a to the base b.

If by log_2 3 you mean log of 3 to the base 2 = log 3 to base 10/ log 2 to the base 10 = 0.4771/0.301 =1.585.

log4 to base 10/ log3 to base 10 = 0.6021/ 0.4771 = 1.261

log 5 to base 10/log 4 to base10 = 0.699/0.6021 = 1.161
answer is 1.585x1.261x1.161 = 2.32

log2(3) * log3(4) * log4(5)

Convert to natural logarithms by putting all of the bases on the bottom and arguments on the top:

= (ln(3) * ln(4) * ln(5)) / (ln(2) * ln(3) * ln(4))

Now cancel out the ln(3)'s and the ln(4)'s, since they are the same:

= ln(5) / ln(2)