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Find the exact value of x Logarithms

  • Thread starter LiHJ
  • Start date
  • #1
43
2

Homework Statement



Find the exact value of x if:

Homework Equations


(3x)lg3=(4x)lg4.


The Attempt at a Solution


3lg3xlg3=4lg4xlg4
(xlg3)/(xlg4)=(4lg4)/(3lg3)
xlg3-lg4=(4lg4)(3-(lg3))
xlg(3/4)=(4lg4)(3lg(1/3))

Please help me, Im stuck here!

Homework Statement





Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution


Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
ehild
Homework Helper
15,427
1,824


Write both sides of the original equation as power of 10, and compare the exponents (which is the same as taking the lg of both sides)
So you get

lg(3)lg(3x)=lg(4)lg(4x)

that is, (lg3)2+(lg3) lg(x)=(lg4)2+(lg4)lg(x)

Isolate lg(x), use the identity a2-b2=(a-b)(a+b) and simplify. You get lg(x) as the logarithm of a number, from which the exact value of x is found.

ehild
 
Last edited:
  • #3
I like Serena
Homework Helper
6,577
176


If xa=b, then x=b(1/a).
 
  • #4
43
2


Thank you so much echild. The answer is (1/12)
 
  • #5
ehild
Homework Helper
15,427
1,824


Exactly! Well done!

ehild
 

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