Question

If I knew all the other values except for n, how would I solve for n in this equation: a_n=a_1 r^((n-1) )

Answer 1

Here is the equation in a better format

Answer 2

best way would be to take natural logarithm on both sides

Answer 3

and use lograthim properties.

Answer 4

is there a simpler way to do it? Because I haven't learned how to do that yet

Answer 5

specifically you can use log(ab) = loga + logb property here

Answer 6

okat let me think

Answer 7

ok thanks

Answer 8

Usually, when you are solving for an exponent, you need to use logarithms.

Answer 9

\[a _{n}/ a _{1} = r ^{n-1}\]

Answer 10

Solve LHS. and transform it to a form which is similar to RHS. Then compare

Answer 11

Yes I think mathstudent55 is true. But there's one exception, if a_n/a_1 can be written as r^x, then x=n-1. That's the case I can think of solving this without using logarithm.