Question

How to solve Exponential Equations? Giving examples in one second

Answer 1

\[2^{2x-1}=8\]

Answer 2

\[5^{1-y}=5^{2y-5}\]

Answer 3

whoa, one at a time please

Answer 4

let's look at the last one

Answer 5

okay sorry just trying to give 2 different examples

Answer 6

\[5^{1-y}=5^{2y-5}\]we can take the log base 5 of both sides
what will happen

Answer 7

I have no clue. What is the log base? Sorry

Answer 8

a log is the inverse property of an exponent
log base 2 of 8 :\[\log_28\]is basically asking
"2 to what power equals 8?"
the answer the that question is 3, so we find that\[\log_28=3\]

Answer 9

in general this means that\[\log_ax=y\iff x=a^y\]which means that\[\log_a(a^x)=x\](i.e. the log "undoes" the exponential if they have the same base)

Answer 10

this is true with the 8 because we could write\[\log_2(8)=\log_2(2^3)=3\]so we come to the same conclusion

Answer 11

so here we have\[5^{1-y}=5^{2y-5}\]so we are going to take the log with the same base as the exponent (5) to "undo" the exponential

Answer 12

so how would we "undo" the exponential?

Answer 13

by taking the log base 5 of both sides\[\log_5(5^{1-y})=\log_5(5^{2y-5})\]which just leaves\[1-y=2y-5\]which can be solved for y

Answer 14

important note!!!!:
this only works when the bases are the same...
we took the log base 5 because everything was to the 5 to some power, otherwise this would not work

Answer 15

okay that makes more sense. What would you do next?

Answer 16

solve for y

Answer 17

how?

Answer 18

How would you solve for y?

Answer 19

How would you solve for y?

Answer 20

if the bases are the same so exponents must be the same..

Answer 21

if the bases are the same so exponents must be zero..

Answer 22

for second
1-y=2y-5

Answer 23

for the first one
\[2^{2x-1}=2^3\]
2x-1=3

Answer 24

so the answer for the second problem would be 1-y=2y-5?

Answer 25

not answer you need to find out y

Answer 26

6=3y
3=y
this is the answer.

Answer 27

I mean 2=y

Answer 28

Oh ok i see. will you be on tomorrow?

Answer 29

god knows it (:

Answer 30

Ok. Any particular time? Would love for you to help me some more if you are willing? Please. Thank you so much!

Answer 31

If I am here I'll try my best..

Answer 32

Okay! thank you! Hopefully we will talk tomorrow!