# Need help with a basic equation.

1. Sep 10, 2014

### christian0710

Hi I don't understand why this is true:

If you have the function logS = a -0,0018t
and you raise both sides of the equation in 10 you should get

S = 10^(a) - 10^(-0,0018t)

but in my book they get

S= 10^(a - 0,0018t)

When you raise both sides of the equation in 10, should you not raise the individual terms on each side and NOT the whole side?

2. Sep 10, 2014

### HallsofIvy

No, you shouldn't! 10^(a+ b)= (10^a)(10^b) NOT "10^a+ 10^b".

You "should" learn the rules of of exponents:
x^(a+ b)= (x^a)(x^b)
and
(x^a)^b= x^(ab)

3. Sep 10, 2014

### Ray Vickson

You seem to think that 10^(a-b) = 10^a - 10^b. Why don't you check this out for yourself? If a = 2 and b = 1, we have c = a-b = 2-1 = 1, so 10^c = 10^1 = 10. Do you agree so far? Now 10^a - 10^b = 10^2 - 10^1 = 100 - 10 = 90. OK still? So, now: do you really think that 10 = 90?

In general, what is true is that $10^{a+b} = 10^a \times 10^b$ and $10^{a-b} = 10^a \div 10^b$. In fact, that is the whole point of logarithms: you can do multiplication or division by addion or subtraction of logarithms.