Question

10^x+4=1000 10^x+4=1000 @Mathematics

Answer 1

logathirmic

Answer 2

is the x+4 all in the exponent of not?

Answer 3

*or not

Answer 4

yes

Answer 5

alright one sec

Answer 6

There's two ways to do this but I'll just show you the way I think is easier.

So the equation is:
\[10^{x+4}=1000\]

First I would manipulate the right side of the equation (1000), so that it becomes an exponent with a base of 10:
\[1000=10^{3}\]

Now you have:
\[10^{x+4}=10^{3}\]

The reason we do that is so that now we can take the base-10 log of both sides to greatly simplify the equation.

By definition:
\[\log_{10} (10^n)=n\]

So when we take the log of both sides we get:
\[\log_{10}(10^{x+4})=\log_{10}(10^{3})\]
\[x+4=3\]
\[x+4-4=3-4=-1\]

So the final answer is:
\[x=-1\]

Checking our answer:

\[10^{-1+4}=10^{3}=1000 \rightarrow \sqrt{}\]

Answer 7

Sorry its so long but I wanted to be sure I fully explained it