Question

Question #9b04c

Answer 1

`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`

Answer 2

`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`