need logrithmic help for math!!?

Question

log16 4

i know the answer is 1/2 but how do you get it?

and

log2 1/32

know the answer is -5 but how do you get it?

Answer 1

To start off, let log (base 4) 16 = 2. That implies that (4)² = 16.

To find log(16) 4, let's express 16 as a power of 4, then things will become much clearer.

*** log(16) 4 = log [(4)²] 4. Let's call this logarithm y.

Then the above equation implies [(4)^2]^y ** = 4^(2y) = 4^(1), which implies that 2y = 1, and that y = 1/2.
**Recall that one of the laws of exponents says that for any base a, (a^m)^n = a^(mn). We use this fact above to find what y must equal if 2y = 1.

Now, since 16 = (4)², we can substitute it back into the triple starred equation above to get this:

log [(4)²] 4 = log(16) 4 = y = 1/2.

Therefore, log(16) 4 = 1/2.

log(2) 1/32 = -5 because log(2) 1/2 = -1 and 1/32 = (1/2)^5.

Note that we can write 1 as 2º, since any number to the zero power equals 1. Then, from one of the laws of exponents, 1/32 = 2º / 2^5 = 2^(0-5) = 2^(-5).

Answer 2

When you do logarithms you are looking for the exponent.
So log5 125 would be 3 because 5^3=125

Now when you look at your 1st problem
log16 4, you might notice that the square root of 16 is 4 the exponent for square root is 1/2
16^1/2=4

The 2nd problem
log2 1/32, you might notice that 2^5=32 but you need a fraction with the denominator as 32 so the exponent is negative
2^-5=1/32

I hope this helps

Answer 3

The answer to the first one is 1/2 because 16^(1/2)=4.
The answer to the second one is -5 because 2^-5=1/2^5=1/32.

Answer 4

Okay, first, you have to think about what a logarithm is. Let's say you have b^x = n (b to the xth power == n). The logarithm is the opposite: log_b n = x (log base b of n == x).

log_16 4 = what power you have to take 16 to to get 4 (1/2)
log_2 1/32 = what power you have to take 2 to to get 1/32 (-5)

Normally, in math, you'll be using natural logs, which is just log_e (where e is an irrational number approximately equal to 2.718281828459).

Answer 5

The first one you do log4\log16 = 1\2

The second one you do log(1\32)\log2 = -5

Answer 6

im guessing its log base 16 to the 4

log4/log16=1/2

log(1/32)/log2= -5

Answer 7

hahahahahahaha