evaluate the following expression: log base 8 of 32?

Question

and if you can figure this out, can you please explain how to get this answer, preferably without the use of a calculator. thanks!

Answer 1

log8(32) = x where 8^x = 32

8^1 = 8 and 8^2 = 64, so 1 < x < 2 (just to get an idea)

log8(32/8) = x -1

log8(4) = x - 1

2^3 = 8 so log8(2) = 1/3 so log8(4) = 2/3

x - 1 = 2/3 or x = 1-2/3 (5/3)

Answer 2

OK, the definition of a = log base n of x is x = n^a. So here, the question is, to what power do you have to raise 8 to get 32? The answer is **not** 4, of course. However, one of the rule of logarithms is that

log(b/c) = log(b) - log(c). And 32 *2 =64. So here,

log base 8(32) = log base 8 (64/2)

= log base 8 (64) - log base8 (2)

Since 2 is the cube root of 8, we know that
log base8(2) = 1/3

Hence, the right-hand side of the above equation becomes just:

1 - 1/3, or 1 and 2/3, or 1.66666............

Answer 3

the answer is a million/3 There are 2 concepts to attempt this: a million) take the log of each and every section. you'll finally end up with this: log (8^x) = log (2) utilizing the exponent rule of logarithms: x * log (8) = log (2) divide each and each and every section through log(8) log(2) / log(8) = x your calculator will do something else 2) what does 8 have in common with 2? 8 = 2^3 so: (2^3)^x = 2 2^(3 * x) = 2^a million 3x = a million x = a million/3

Answer 4

log8(32), it means that a number that 8 elevated to x number will have as result 32.
it is 8^x=32. x=5/3

Answer 5

log means log to base 8:-
y = log 32
8^(y) = 32
Can then take logs to any base:-
y log 8 = log 32
y = log 32 / log 8
Assume base 10 for calculation:-
y = 1.505 / 0.903
y = 1.67