what is the relationship between exponets and logarithms?

Question

emmyma · Answer

Hi!

Exponentials and logarithms are inverse of each other. If you take the graph of y = 10 ^ x and flip it over the diagonal line y=x, what you get is the graph of "y = log10(x)" by which I mean the log base 10 of x. 

Good luck! Make sure to give me a medal if I helped.
:)

emmyma · Answer

Simply put, logs are the inverse of exponents. Log base b of (y)= x is the same as b^x=y.

anonymous · Answer

Thank You emmyma! So this is like addition is the opposite of subtraction and division the opposite of multiplication?

emmyma · Answer

Basically, that's it! Great job :–)

unklerhaukus · Answer

$$\log_bx=y\quad\iff\quad x=b^y$$

$$\log_a(xy)=\log_a(x)+\log_b(y)\quad\iff\quad a^xa^y=a^{x+y}$$
$$\log_a(a)=1\quad\iff\quad a^1=1$$