URGENT.. I CAN'T FIGURE THESE OUT.... I am going CRAZY!!!!!?

Question

For questions 1-2, convert to logarithmic equations. For example, the logarithmic form of "2^3 = 8" is "log2^8 = 3".

1.16^3/2 = 64

2.e^x = 5

For questions 3-4, write the logarithmic equation in exponential form. For example, the exponential form of "log^5 25 = 2" is "5^2 = 25".

3.log^3 27 = 3

4.log^125 25 = 2/3

Answer 1

1 . 16^3/2 = 64
log 64 (base 16)= 3/2
2 . e^x = 5
log 5(base e) = x

3 .log 27 (base 3) = 3
thus 3^3 = 27
4. log 25 (base 125) = 2/3
thus 125^2/3 = 25

Remember
log a (base b) = x means a = b^x
and a^b =x means b = log x (base a)

Answer 2

Generally: log to the base a of n = x means a ^x = n.

(1) 16^3/2 = 64 here a is 16, x is 3/2 and n is 64 which means log to the base 16 of 64 = 3/2.

Sorry I can't type these as you have to write them.

(2) e^x = 5 here a = e, x = x and n = 5 which means
log to the base e of 5 = x

Now we are doing it the other way round.

(3) This should be log to the base 3 of 27 = 3 . Here a = 3, x = 3 and n = 27. Which means in exponential form 3^3 = 27. This is correct because 3 to the power of 3 is 3x3x3 which is 27.

(4) This should be log to the base 125 of 25 = 2/3. Here a = 125, x = 2/3 and n = 25. Which means in exponential form 125^ 3/2 = 25. This is correct because 125^3/2 means 125 to the power of 2/3 which means the cube root of 125 squared which is 25.

Hope this has helped you.

Answer 3

@1 : 16^3/2 = 64 (Note the 3/2,using the denominator,u can get x²=16,so x is 4.Next ,you are suppose to find the numerator.So it's 4³ = 64)

@2: e^x=5
Ln5=x (Use a calculator to find the value of Ln5)

@3: log^3 27 =log^3 3³
=3log^3 3
=3(1)
=3

@4: log^125 25=log^125 125^2/3
=2/3(log^125 125)
=2/3(1)
=2/3