I need some serious help. This is my last assignment!! :-)?

Question

I need some serious help with logarithims.
I need to convert these equations to logarithmic equations

1. 16^3/2 = 64
2. e^x = 5

I need to write these logarthimic equations in exponential form.

3. log3 27 = 3 (Imagine the 3 is subscripted below the log)
4. log125 25 = 2/3 (Imagine the 125 is subscripted below the log)

Answer 1

It's been a while since I've done maths and I'm not exactly sure how you're expecting the answers/presentation of the answers of these questions.

1. Apply log to both sides -> bring down the power3/2 -> bring the logs to one side.
16^3/2=64 -> log(16^3/2)=log64 -> (3/2)log16=log64 -> 3/2=(log64)/(log16)

2. Apply ln to both sides -> bring down the powerx.
e^x=5 -> lne^x=ln5 -> xlne=ln5 -> x=ln5

For 3 and 4, basically change the base of the log function. So (using the same notation as yours in writing the log base):

3. log3 27=3 -> (log10 27)/(log10 3)=3

4. log125 25=2/3 -> (log10 25)/(log10 125)=2/3


Hope it helped.

Answer 2

1. 16^3/2 = 64
You didn't mention what log base you wanted to use. Let's try the base 4.
Log (base 4) of 16 is 2
So Log (base 4) of 16^3/2 = 3/2 * 2 = 3
Log (base 4) 64 = 3

2 . e^x = 5
Here we'll use the natural log base, ln

ln e^x = x
ln 5 = 1.6094
So x = 1.6094

3. Log base 3 of 27 = 3
in exponential form
3^3 = 27

4. Log base 125 of 25 = 2/3
in exponential form
125^2/3 = 25

Note what that means: If you take the exponent 2/3 to mean
squaring the base (the "2" part of 2/3) and then taking the cube root of the result (the "1/3" part of 2/3) you get 25.

It doesn't matter what order you do the operation in.

The cube root of 125 is 5.
5 squared is 25

Hope this helps you get a better understanding of the process, which is what's really important, not the answer to a particular problem.

Answer 3

1)

16^(3/2) = 64

(3/2) log 16 = log 64(rule loga^b = b loga)

2)

e^x = 5

taking logs both sides

x ln(e)e = ln5

x = ln 5 (rule ln(e) e = 1 Note: log of any number to the base

of same number = 1)

3)

log[3]27 = 3

3^3 = 27 (rule : if log[a]b = c, then a^c = b)

4)

log[125]25 = 2/3

(125)^(2/3) = 25

Answer 4

1. 3/2* log 16 = log 64.
(log of a^x = x log a).
2. x = log 5.
(log of e^x = x)
In these 2 problems, log means natural log.
3. 3³ = 27.
If log_a x = b then a^b = x.
So the answer to #4 is
125^2/3 = 25.
The other 2 rules you need to remember are
log(ab) = log a + log b
and log(a/b) = log a - log b.