Posted by **Alley** on Saturday, April 6, 2013 at 8:50am.

Solve the equation

log[14](x+49) - log[196] x=1

- solve the equation -
**MathMate**, Saturday, April 6, 2013 at 9:26am
Given

log_{14}x+49 - log_{196}x = 1

We will use a lemma that

log_{a}x=log_{a²}=x²

Since 196=14², we write above as

log_{14}x+49 - log_{14²}x = 1

Then

log_{14²}(x+49)² - log_{14²}x = 1

Rewrite using laws of logarithm:

log_{14²}(x+49)²/x = 1

Using the alternate form from the definition of logarithms,

(x+49)^2/x = 14²

Transpose and solve for x to get

(x-49)²=0, or

x=49

- solve the equation - typo -
**MathMate**, Saturday, April 6, 2013 at 9:28am
We will use a lemma that states:

log_{a}x = log_{a²}x²

The proof of the lemma is left to you as an exercise, if it was not already covered in your course.

## Answer this Question

## Related Questions

- math - solve for x without using a calculator 5^(x+1) = 25 i know that x would ...
- calculus - Please help me solve this equation. log[2](3)+log[2](x)=log[2](5)+log...
- algebra - logarithms Solve the following equations 3^x-2=6 Add 2 to both sides ...
- Advanced Functions/ Precalculus Log - 1. Evaluate 4^(log base4 64) + 10^(log100...
- math - Logarithm!!! Select all of the following that are true statements: (a) ...
- Re: Algebra II - How to solve Log (9x+5) - Log ((x^2)-1) = 1/2 16 16 (The 16 is...
- Math - h(x) = log (6x+5/7x-4) Find a formula for the inverse function h^-1(x) h...
- check! - here is the question: log5(x-4)= log7x solve for x. These are just base...
- Trigonometry - Solve for x to the nearest hundreth and can you explain how you ...
- TRig WIth LoGs help1!! - i have problem i can't solve and the book is no help.. ...