Question

how do you solve log base 64 of 0.5 = x?

Answer 1

definition of log is
base ^ x = 0.5, so
64^x = 0.5
take the log of both sides:
log(64^x) = log(0.5) .
you can pull exponents in logs into the front:
x log(64) = log(0.5)
x = log(0.5)/log(64)
x= -1/6

Check
64^(-1/6) = 1/2
:) Hope that helps!

Answer 2

i don't understand this :/

Answer 3

if i have log base x = a, that means
base ^a = x
Does that much make sense? If so I can keep going :)

Answer 4

ok yea

Answer 5

okay, so plugging your numbers, you have 64 ^x = 0.5
We are interested in solving for x, and there is a tricky way of doing that.

Answer 6

Notice that at the moment, the x is part of an expression that is kind of weird to undo since it is the exponent. To undo it, we use a function that allows us to drag down the exponnet as a coefficient of the expression. So as review,
if I have:
log(a^b), this is the same as
b *log(a)
Does that much make nse?

Answer 7

ok yeaaaaaa

Answer 8

okay yay. so now we apply that idea to what we were doing.
If 64 ^x = (0.5)
I can take the log of both sides
log(64^x) = log(0.5)
And similar to the general case I explained, this is
x * log(64) = log(0.5)
Yeah?:)

Answer 9

ok yesssssss

Answer 10

wow my computer just froze, let me type that again

Answer 11

so now we are just solving for x, which is totally possible because the x term is now isolated. we can think of log (64) and log (0.5) like numbers because the log of a number is another number. So we can divide each side by log(64)
x*log(64) = log(0.5)
x = log(0.5)/log(64)
And then no one knows those things off the top of their head unless they work with logs a lot, so the typical person will evaluate the right hand side expression using a calculator
x = -1/6
I hope that makes sense now!

Answer 12

okay i get it now ! thank you so much !(:

Answer 13

:) No problem!