Asked by Mitch n' Joey

Write the expression as a single logarithm.
log_3 40-log_3 10

I'm completely confused with logarithmic equations!! Can someone please please help me understand?

Answers

Answered by Steve
since loga - logb = log(a/b), we have

log_3 40-log_3 10
= log_3(40/10)
= log_3(4)

logs are just exponents in reverse. You know that

x^6/x^4 = x^(6-4)

log_3(40) is the power of 3 you need to get 40

since ^ and log are inverse operations,

3^(log_3(x)) = x
log_3(3^x) = x

just as
√x^2 = (√x)^2 = x
(x/2)*2 = (x*2)/2 = x
(x+2)-2 = (x-2)+2 = x
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