another alegra II problem?

Question

3 logb(x) = logb (64) i dunno how to do this

Answer 1

OK, here's a rule to remember:

a log b = log b^a

So:
3 logb(x) = logb (64)
logb(x) = 1/3 * logb (64)
logb(x) = logb (64^(1/3))
logb(x) = logb (4)

Now, you can undo the logb on both sides...
x = 4

Answer 2

When using logarithms, the log of any number to an exponent is equal to the log of that number times the exponent:

log (x^y) = ylog(x)

Therefore:

3 logb(x) can be written as logb (x^3).

and

x^3 = 64

x = 4

Answer 3

Remember, 3 log_b x = log_b x^3.
So log_b x^3 = log_b 64.
Take the antilog of both sides. Then
x^3 = 64
x = 4.
Hope that helps.