How do you evaluate #log _ { 9 } ( \frac { 9^ { 5} } { 7^ { 4} } )#?

Question

879 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-21T19:38:01

#5-log_9(7^4)~~1.46#

The logarithm of a fraction is the log of the numerator, minus the log of the denominator.

#log(a/b)=log(a)-log(b)#

So #log_9(9^5/7^4)=log_9(9^5) - log_9(7^4)#

What power of 9 gives us #9^5#? 5.

We now have #5-log_9(7^4)#

#log_9(7^4)# doesn't give us a nice integer answer, so you'll have to use a calculator to get approximately 3.54.

#5-3.54=1.46#