Question

solve each equation. give an exact solution and a four-decimal place approximation.
7. 5^(2x)=12
8, ln(x+3)=2
9. 4^(x-2)=3
10. 2^(x-3=6^(1-2x)

Answer 1

@ganeshie8

Answer 2

if u see exponents in the equation,
and if u dont see logs anywhere, then taking log both sides is a good idea

Answer 3

\(\large 5^{2x}=12\)

take log both sides

\(\large \log( 5^{2x})= \log (12)\)

Answer 4

next, u need to knw few log properties :

\(\large \log_a (b)^m = m ~\log_a b\)

Answer 5

use it

Answer 6

how do i break down 12

Answer 7

\(\large 5^{2x}=12\)

take log both sides

\(\large \log( 5^{2x})= \log (12)\)

\(\large 2x~\log( 5)= \log (12)\)

Answer 8

divide both sides by \(\log (5)\)

Answer 9

\(\large 5^{2x}=12\)

take log both sides

\(\large \log( 5^{2x})= \log (12)\)

\(\large 2x~\log( 5)= \log (12)\)


\(\large 2x = \frac{\log (12)}{\log(5)}\)

Answer 10

use ur calculator and find out both logs on right hand side

Answer 11

and divide

Answer 12

log12 is 1.079181246 and log5 is .6989700043

Answer 13

yes, divide them

Answer 14

log 12/log5 is 1.543959311

Answer 15

yes !

so,

\(\large 5^{2x}=12\)

take log both sides

\(\large \log( 5^{2x})= \log (12)\)

\(\large 2x~\log( 5)= \log (12)\)


\(\large 2x = \frac{\log (12)}{\log(5)}\)

\(\large 2x = 1.543959311\)

Answer 16

solve \(x\)

Answer 17

1.543959311/2 is .7719796555

Answer 18

correct ! round it as asked...

Answer 19

1

Answer 20

whut

Answer 21

.7719796555

rounded to four decimal places is

.7720

Answer 22

ohhh ok i didnt learn that

Answer 23

its time for lunch when i come back i will let you know so we can finish and thank you so much

Answer 24

enjoy ur dinner !

Answer 25

lol here its dinner time in india :)

Answer 26

im back

Answer 27

@ganeshie8

Answer 28

hey sorry, missed this...

Answer 29

for next question,

base of ln is always \(e\)

Answer 30

\(\large \ln(x+3)=2\)

is same as

\(\large \ln_e(x+3)=2\)

Answer 31

change it to exponent form...

Answer 32

e^2=x+3

Answer 33

yes, solve \(x\)

Answer 34

and keep in mind, "e" is just a NUMBER, like "pi"

Answer 35

x=1

Answer 36

how ?

Answer 37

e^2 = x + 3

subtract 3 both sides

e^2 - 3 = x

Answer 38

5.389

Answer 39

try again

Answer 40

http://www.wolframalpha.com/input/?i=e%5E2-3

Answer 41

you should get

x = 4.3891

Answer 42

i see it now