Question

How do I solve this exponent problem?

Answer 1

\[3^x-2(3)^{1-x}=5\]

Answer 2

compute 3^(2x+1)

Answer 3

can you split 3^1-x in to two exponents?

Answer 4

great @FaiqRaees - this is the first step sure

Answer 5

can multiply 3^(x+1) on every side?

Answer 6

A^m * A^n = A^m+n

Answer 7

then I can get 3^(2x+1) on the left side

Answer 8

first its not 3^2x+1 its 2(3^1-x) and no. After this you can make the l.h.s a complete exponent of 3

Answer 9

ok if i split it i will get 3^1 x 3^-x

Answer 10

yes which will be \[3/3^x\]

Answer 11

now multiply the two with the fraction.

Answer 12

-6/3^x

Answer 13

and when you've done it make an equation y=3^x and then subsitute y in place of 3^x and then you've gotten a quadratic equation. Solve it find values of y and then use them to fund the values of x

Answer 14

find*

Answer 15

wait when i've done what? do i multiply the whole thing by 3^x now to remove the fraction?

Answer 16

yes

Answer 17

now I have 3^(2x)-6=3^(x)(5)

Answer 18

do i solve for x and put it back into 3^(2x+1)

Answer 19

or do i do that directly from the equation not sure

Answer 20

actually i see what you mean by quadratic equation i set 3^x=u

then i get u^2-5u-6=0

i get 6,-1

do i set those 2 numbers to 3^x?

Answer 21

yes

Answer 22

so i solve for 3^x=6 and -1?

Answer 23

yes

Answer 24

btw you have to neglect -1 because no number when squared to any number results in a negative number.

Answer 25

how do i solve for x here again lol

Answer 26

is \(\large\bf 3^x-2(3)^{1-x}=5\) it? just clarifying

Answer 27

apply logarithm

Answer 28

yes

Answer 29

should i walk you through the logarithm part or you know how to apply them

Answer 30

i remember the exponential form to log form, this becomes log3(6)=x but i actually forgot how to plug that into calculator

Answer 31

use the log change of base rule, to make it either ln or base10

Answer 32

yeah i got it

Answer 33

its just log(6)/log(3)

Answer 34

yeap

Answer 35

so answer we get 108

Answer 36

hmmm log(3)/log(6) gives me something else =|

Answer 37

you have to use log 6 /log 3

Answer 38

and answer will be 1.630929

Answer 39

108 i meant for the problem

Answer 40

ohhhh rats... yeah.. mistead there

Answer 41

ohhh right