Question

which of the following is the solution of \[\log _{x-5}0.001= -3\]

Answer 1

you have to use base change formula... Log(0.0001)/log(x-5)=-3....can you do it now?

Answer 2

yes, thank you

Answer 3

YW :)

Answer 4

Is the answer 13?

Answer 5

i guess no

Answer 6

Then I'm confused

Answer 7

just you can equate log both the sides by \[\log(10^{-4})= \log(x-5)^3....(x-5)^3=0\] now i hope you can do this

Answer 8

I'll try

Answer 9

That's a bit too complicated. Using the properties of log,
\[log_ba=c\]\[a=b^c\]\[\sqrt[c]{a}=b\]

Answer 10

How do I plug the problem into that?

Answer 11

\(\huge log_{x-5} (0.001)=-3 \) means \(\huge (x-5)^{-3}=0.001 \)

so can you solve for x from here?

Answer 12

Do I multiply x-5 to the negative 3rd power? or do I solve using "Solving Equation with Unequal bases?

Answer 13

nah.... just change that right side to a power of 10...
\(\huge (x-5)^{-3}=0.001 \)
\(\huge (x-5)^{-3}=10^{-3} \)
\(\huge x-5=10\)

Answer 14

after that do I add 5 to each side so it will become\[x=15\]

Answer 15

yep...

Answer 16

thanks

Answer 17

yw...:)

Answer 18

So its x =15