# log help

#### goosey00

##### Member
In log x + (x-15)=2 and I have to convert it to an exponental. On the practice one they said in the form of log(small)M+log(small)aN=log(small)aM*N
so log(small)ax a^x=x
a=10
Why in this equation does a=10?? I don't understand. In the equation above I understand it being x(x-15)=2 just not the a=10 part Please help

#### Jameson

Staff member
Re: log./^ help

In log x + (x-15)=2 and I have to convert it to an exponental. On the practice one they said in the form of log(small)M+log(small)aN=log(small)aM*N
so log(small)ax a^x=x
a=10
Why in this equation does a=10?? I don't understand. In the equation above I understand it being x(x-15)=2 just not the a=10 part Please help
Hi goosey00,

Should there be another log? You wrote "log x + (x-15)=2" but I think it might be "log x + log(x-15)=2"

#### goosey00

##### Member
your right. BTW-the other day when we had that long thread, my teacher said I didn't even have to go as far as I did. All that time we spent-really??? Oh well.

#### Jameson

Staff member
Ok, so we have $$\displaystyle \log x + \log (x-15)=2$$. A rule you need to know, among a couple of others, is $$\displaystyle \log a +\log b = \log (ab)$$. You can go the other way as well. So combine the two log expressions into one and then use the definition of log to rewrite the equation. What do you get for that?

#### goosey00

##### Member
Im sorry Im still confused. The end is -2(a*b) right. ??

#### Jameson

Staff member
$$\displaystyle \log x + \log (x-15)=2$$

$$\displaystyle \log[x*(x-15)]=2$$

Assuming log x means base 10, then $$\displaystyle 10^2=x(x-15)$$

Can you go further?

#### goosey00

##### Member
SO, is the rule of a base is 10. You wrote assumed. Thats the confusing part is the 10. I can solve it from there. I just am missing something.

#### Jameson

Staff member
SO, is the rule of a base is 10. You wrote assumed. Thats the confusing part is the 10. I can solve it from there. I just am missing something.
The way logarithms are defined is $$\displaystyle \log_{a}b=x \implies a^x=b$$ When there is nothing written in subscript then we can assume it's 10 (in higher math it could mean "e"). For this problem I think it's safe to say the base is 10. However, you need to remember the definition above in order to switch between the log form and exponential form of an expression.

Did your teacher explain what logarithms are and how you can use certain properties to manipulate them?

#### goosey00

##### Member
not really but what you just said completely makes sense now. Thanks again. Jenny