Question

I'm trying to figure this out, but I can't seem to get it right. It says:

Answer 1

Which of the following is the solution of log x+3 (.001)=-3

Answer 2

I tried putting it in exponential form, and looked it up, but every time I change it to exponential form, I get: (x+3)^-3=.001, and I'm pretty sure that's not right. How do I do this? It's getting confusing.

Answer 3

is it \[\log(x+3)^{.001}=-3\]?

Answer 4

Use \[\large\log_bx=y\quad\iff\quad x=b^y\]

Answer 5

Ummm... the x+3 looks like a base, and .001 isn't an exponent, so I don't think so

Answer 6

oh , like this?

\[\log_{x+3}(.001)=−3\]

Answer 7

Yes!

Answer 8

Also, I've seen a similar formula you gave, only it looks like this: y=b^x >> x=log b (y). What's the difference between the two?

Answer 9

um there is no difference i just choose x where they chose y and visa versa.

\[\large y=b^x\quad \iff\quad \log_b (y)=x\]

hmm, can you express .001 as a power of ten?

Answer 10

That would be 10^-2, right?

Answer 11

.1 is 10^-1

.01 is 10^-2
so
.001 is 10 ^-...

Answer 12

Oh 10^-3. Whoops. Okay, got it.

Answer 13

Right , so

\[\log_{x+3}(.001)=−3\\\log_{x+3}(10^{-3})=−3\]

Answer 14

So...
10^-3=(x+3)^-3 ?

Answer 15

yes!

Answer 16

So when I'm solving this, can I cancel the exponents out, or would that be bad?

Answer 17

that's correct
the exponents on both sides are the same so they can cancel

10 = x+3

Answer 18

So x=7. Okay, got it. Thank you for helping me!! That really fixed my confusion.

Answer 19

yay you got it !