Question

use the properties of logs to solve log_2(10x-x^2)=4.. the answers are in the back of the book which are 2 and 8.. but im not sure how to get there,, please post the steps! thank you!!

Answer 1

10x-x^2=2^4
10x-x^2=16
x^2-10x+16=0
x^2-8x-2x+16=0
x(x-8)-2(x-8)=0
(x-8)(x-2)=0
x=2 or x=8

Answer 2

@mathhelpplease9976

Answer 3

how about the log_2 part i can just drop that?

Answer 4

2 is the base of log

Answer 5

so i can just cross it out?

Answer 6

\[\log_{a} b=x \]

Answer 7

the b=a^x
it is property of log

Answer 8

got it????

Answer 9

sweet thank you! got it!!

Answer 10

canu answer one more question

Answer 11

wlcme :)))

Answer 12

yeh sure

Answer 13

solve log_2(log_3(x))=2 .. answer is 81

Answer 14

yeah buddy u grabbed it

Answer 15

no no like that is the answer in the back of the book.. but i dont know how to work it out!! hahaha

Answer 16

log_3(x)=2^2=4
x=3^4=81

Answer 17

where did u get 3^4

Answer 18

got it thank you!!!!

Answer 19

how about factor or use quadratic formula to solve: (5^x)^2-2(5^x)-1=0.. answers in the back of the book is log_5(1+sqrt(2)=ln(1+sqrt(2))/ln 5.. show work please

Answer 20

add and subtract 1
(5^x)^2-2(5^x)+1-1-1=0
(5^x)^2-2(5^x)+1-2=0
(5^x-1)^2=2
(5^x-1)=sqrt2
(5^x)=sqrt2+1
now take natural log both side
ln(5^x)=ln(sqrt2+1)
x*ln5=ln(sqrt2+1)
x=ln(sqrt2+1)/ln5

Answer 21

whyd you subtract and add 1 in the beginning

Answer 22

@gorv

Answer 23

to make perfect square

Answer 24

omg you are so msart.. how do you know all this math ?

Answer 25

*smart

Answer 26

how about.. solve the equation using the one to one property.. 3^x=27^x2.. answer is 0 and 1/3

Answer 27

@gorv

Answer 28

are u asking the whole book lol

Answer 29

first practice on properties of log u will get everything

Answer 30

hahaha ok. im just really bad at them and i have a test soon so trying to understand haha thanks

Answer 31

how wouldi do that if there is x^2 thought on the right side like i know i should get common bases

Answer 32

3^x=27^x2
take log both side
xlog3=x^2log27

Answer 33

r u a math teacher or somethinggg haa

Answer 34

xlog3=x^2 * log3^3 ---------------------3^3=27
xlog3=3x^2*log3
x=3x^2
3x^2-x=0
x(3x-1)=0
x=0
or x=1/3

Answer 35

bro i just love maths....n i m doing my under grad

Answer 36

in math?

Answer 37

dude you are a life saver

Answer 38

no in engineering

Answer 39

i knoe that so i solved it man

Answer 40

hahado u get paid for this or just for fun?