How many different license plates can be made using 4 letters followed by 3 digits selected from the digits 0 through 9, if digits may be repeated but letters may not be repeated?

answer: howdy

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: