log(base 2)x + log(base 4)x = 5?

Question

it turns into 1/log(base x)2 + 1/log(base x)4 = 5 but i'm stuck

Answer 1

change:
log(2) x = ln x / ln 2

log(4) x = ln x / ln 4

Now you have:

ln x / ln 2 + ln x / ln 4 = 5
ln x / ln 2 + ln x / (2 ln 2) = 5

Get a common denominator...
2ln x / 2 ln 2 + ln x / 2 ln 2 = 5
(3ln x) / (2 ln 2) = 5
3(ln x) = 10 ln 2
ln x = (10 ln 2)/3
ln x = ln 2^(10/3)

now take the e on both sides...

x = 2^(10/3)

Answer 2

log(base 2)x + log(base 4)x = 5

Let y = log(base 2) x which gives x = 2^y

y + log(base 4)x = 5

log(base 4)x = 5 - y

x = 4^(5 - y)

2^y = 4^(5 - y)

2^y = 2^(2(5 - y)) (because 2^2 = 4)

Therefore y = 2(5 - y)

3y = 10

y = 10/3

x = 2^y
x = 2^(10/3)

:-D

Answer 3

First you need to seperate the equation into these parts:
Log(base2)x
and
Log(base4)x
then use othe variables such as "a" and "b" for each
a = log(base2)x
b = log(base4)x
so x = 2^a and x = 4^b = (2^2)^b = 2^(2b)
therefore: 2^a = 2^2b => a = 2b
so log(base2)x = 2 * log(base4)x
substitute this in your initial equation and you'll have:
2 * log(base4)x + log(base4)x = 5
=> log(base4)x = 5/3
=> x = 4^(5/3)
=> x = 10.0793

Answer 4

let log(base 2) x = y

then x = 2^y

log (base 4) x = z
x = 4^z or 2^2z

so y = 2z
y+ z = 5
3z = 5
z = 5/3
x = 4^5/3 or 2^(10/3)

Answer 5

log (base 2) x + log (base4) x = 5

log (base 2) x + log (base4) x = 5

log (base 2) x + 1/log (base x) 4 = 5

log (base 2) x + 1/(2log (base x) 2) = 5

log (base 2) x + 1/2 * (log (base 2) x) = 5

log (base 2) x + log (base 2) x^(1/2) = 5

log (base 2) x^(3/2) = 5

x^(3/2) = 2^5

x = (2^5)^(2/3)

x = 2^(10/3)

Answer 6

Since log(base4)x = .5log(base2)x then we get

log(base2)x + .5log(base2)x = log(base2)x + log(base2)x^.5

= log(base2) x^1.5 = 5.

so using both sides as the exponent of 2 gives x^1.5 = 2^5. thus x = (2^5)^(2/3) = 2^(10/3).

Answer 7

raise 2 to both sides

2^(log2(x)+log4(x))=2^5
2^log2(x)*(4^(log4(x)))^(1/2) = 2^5
x(x^(1/2))=2^5
x=2^(10/3)

Answer 8

http://www.mathworld.wolfram.com

Answer 9

log(base2)x+log(base4)x=5
log(base2)x+log(base2^2)x=5
log(base2)x+1/2log(base2)x=5
3/2log(base2)x=5
log(base2)x=10/3
x=2^(10/3)