# How do you find the exponential function f(x)= a^x whose graph goes through the point (3, 1/125)?

##### 1 Answer

Dec 6, 2016

Please see the explanation.

#### Explanation:

Use the logarithm of your favorite base on the function (My favorite is the natural logarithm but base 10 works just as well):

Use the identity ln(a^x) = (x)ln(a):

Divide both sides by x and flip the equation:

Make both sides exponents of the base e:

Use the identity

Substitute 3 for x and 1/125 for

If you prefer a fraction: