How to distribute ln into right side of this equation

[LearninDaMath]

once i get ln on both sides, I'm then supposed to differentiate both sides...but I won't be able to properly differentiate if ln is not applied.

Does ln get applied to the 976, (-1) and 176t? How?

 

[kru_]

You can use the chain rule here.

Treat 976[ (.835)^t - 1] + 176t as a function of t. Then your equation becomes ln( f(t) ). And you can use the chain rule to determine the derivative.

 

[Mark44]

To answer the question in your title, you can't "distribute" ln into a sum, because ln is not a factor.

Distributive property: a(b + c) = ab + ac

BUT
cos(b + c) ≠ cos(b) + cos(c)
ln(b + c) ≠ ln(b) + ln(c)
√(b + c) ≠ √b + √c

cos, ln, and √ are functions - there is no distributive property for functions.