Question

Solve for t. Assume a and b are positive constants.
a=b^t

t=_______

Please explain? Thank you :)

Answer 1

t = logbase(b) a

(you can't do subscripts in this, but when you write it it should look like: log subscript:b normal: a

A logarithm is the opposite of an exponent, so when they ask you to solve for an exponent, the answer is always a log

Answer 2

ohh so does t= ba ?

Answer 3

t =/= ba because the logbase isn't a number on its own, I'm gonna draw you a diagram to show you how it works...one sec

Answer 4

what do you mean by t=/= ba? :/

and okay :)

Answer 5

t does not equal ba

Answer 6

http://www.virtualnerd.com/algebra-2/exponential-logarithmic-functions/logarithms-logarithmic-functions/logarithms-introduction/convert-log-to-exponential

Answer 7

W/o being able to use equation editor, that'll be easier ^^

Answer 8

ohh okay @samarasamara haha wasn't sure what that meant! :P

@agent0smith yeah not sure why the tools still aren't working :/

Answer 9

okay, so I used paint and this isn't super clear, take a look at this and tell me if you still don't get it. The video in @agent0smith 's link looks helpful

Answer 10

okay, yeah it makes sense... i think haha

it's just a rule that you have to memorize right?

Answer 11

Basically, yes, memorize it.

Answer 12

yup, it helps to think of the numbers as moving in a semicircle, the logbase goes to the other side of the equal sign and pushes up the number that the equation is equal to, which then becomes the exponent

Answer 13

ok will do :)

@samarasamara i will try to remember that!! thanks so much!! :)

Answer 14

The other way to remember it is to just take logs of both sides, with the base of the log matching the base of the exponent in the equation

a=b^t

so here you'd take log base b of both sides.

Answer 15

ohh okay thank youu!! :)

Answer 16

t = Log[a]/Log[b]