Question #9b04c

2 Answers
Aug 5, 2017

log_10(1000)=3

Explanation:

I'm assuming that you mean log with base 10. The answer will be different if the base is not 10.

Here are two ways of writing the same expression:

y=log_10(x)

and

10^y=x

y="the power"

10="the base"

x="the answer"

We need to solve for the power, y. Start with the log form:

y=log_10(1000)

Rewrite this expression in index form:

10^y=1000

Rewrite the expression with the same base on both sides:

10^y=10^3

Because we have the same base, the powers must be equal:

y=3

So log_10(1000)=3

See if you can find another way of solving this problem using the following log laws:

log_a(b^n)=nlog_a(b)

log_a(a)=1

Aug 5, 2017

log(1000)=3

Explanation:

Usually log stands for "logarithm base 10" or log_10

A logarithm is a function that returns the power to which you must take the base to get the input.

Or in the case of base 10

log(10^x)=x

and for any base b

log_b(b^x)=x

Since 1000=100times10 and 100=10times10,

then 1000=10times10times10

And by the definition of an exponent

1000=10times10times10=10^3

Then

log(1000)=log(10^3)=3