Question

solve: log 4th root of x=square root log x

Answer 1

\[\log \sqrt[4]{x }=\sqrt{\log x} \]

Answer 2

x=1 , x = e^16

Answer 3

1/4(logx) = (logx)^(1/2)

Answer 4

substitute u = logx and solve the quadratic ... get it ?

Answer 5

you should have u/4 = √u

Answer 6

where did you get the u from

Answer 7

is just a substitution to make the eq solvable ... you've never done substitutions?

Answer 8

no

Answer 9

it's a common technique

Answer 10

teach me it

Answer 11

how would you solve this (xy)^2 + 2xy +1 = 0 ?

Answer 12

if you substitute xy = m (letter doesn't matter ) you'll get
m^2 +2m +1 =0 ... now this is easier to solve ..right?

Answer 13

right

Answer 14

you just have to ... sense ... when is appropriate ... but it is quite common

Answer 15

just like in your problem ... without the substitution would be very difficult to solve it

Answer 16

so you substitue the log for u?(or whtever letter)?

Answer 17

log x = u ...yes

Answer 18

after using some properties of logs

Answer 19

so u^1/2?

Answer 20

u/4 = √u

Answer 21

easier

Answer 22

i got it thannks bro

Answer 23

np