Seven years ago, douglas purchased a $204,000 home with a 30-year mortgage at 4.5%. having recently lost his job, he can no longer afford to make his mortgage payments. if he currently owes $177,533.62 and his lender offered to extend the loan by 7 years at 4.25%, what will be his new mortgage payment?

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:

whew you’re speaking a different language

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