I know that root[3](54)=54^(1/3) but otherwise I don't know how to address these types of problems. How do I solve this, and is there a general way of tackling these problems? Like, if I had ln.75 or ln8/9, for example. These types of problems that I have are all different and I don't understand a general way of looking at them.

opositor5t

opositor5t

Answered question

2022-08-10

Expressing ln 54 3 in terms of ln 2 and/or ln 3
I know that 54 3 = 54 1 / 3 but otherwise I don't know how to address these types of problems. How do I solve this, and is there a general way of tackling these problems? Like, if I had ln .75 or ln 8 9 , for example. These types of problems that I have are all different and I don't understand a general way of looking at them.
thanks.

Answer & Explanation

Deja Navarro

Deja Navarro

Beginner2022-08-11Added 17 answers

There are three properties to know:
ln ( a b ) = ln a + ln b
ln ( a b ) = ln a ln b
ln ( a b ) = b ln a
The rest is just putting things together, and using these multiple times. In particular, you'll probably find it useful to know that 54 = 2 3 3 ; now expand a few times.
Matonya

Matonya

Beginner2022-08-12Added 2 answers

As ln a m = m ln a         ( 1 ) and ln a + ln b = ln ( a b )         ( 2 ) when logarithms remain defined
Now, 54 3 = 54 1 3 use ( 1 )
Again, 54 = 2 3 3 Now use ( 2 )

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