SOLUTION: If: log₂x + log₄x + log₁₆x = 21/4 find x.

Question 1206690: If:
log₂x + log₄x + log₁₆x = 21/4
find x.
Found 5 solutions by MathLover1, greenestamps, math_tutor2020, MathTherapy, Edwin McCravy:
Answer by MathLover1(20855)   (Show Source): You can put this solution on YOUR website!
....change to base

...use common denominator

...both sides divide by

...if log same, then

Answer by greenestamps(13327)   (Show Source): You can put this solution on YOUR website!

Ouch!!!

The solution method shown by the other tutor is valid, but WAY more work than needed....

The bases of the logarithms are all powers of 2, making for a quick and easy path to the answer.

, so
, so

So

Then

ANSWER: 8

Answer by math_tutor2020(3835)   (Show Source): You can put this solution on YOUR website!

Answer: x = 8

Work Shown

w = log(x)
v = log(2)

2v = 2*log(2) = log(2^2) = log(4)
4v = 4*log(2) = log(2^4) = log(16)

Change of base rule

Answer by MathTherapy(10806)   (Show Source): You can put this solution on YOUR website!

If: log₂x + log₄x + log₁₆x = 21/4 find x. ---- Changing ---- Multiplying by LCD, 4 ----- Dividing both sides by 7 ----- Converting to EXPONENTIAL form

Answer by Edwin McCravy(20077)   (Show Source): You can put this solution on YOUR website!

find x. Since , Edwin

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