Posted by **james** on Monday, March 19, 2012 at 4:23am.

Solve for x in the following equations. (4 marks)

log3(x - 5) + log3(x + 3) = 2 <--- both log3.. 3 is subscript

log7x + log7(x - 1) = log72x <--- all log7.. 7 is subscript.

- math -
**Reiny**, Monday, March 19, 2012 at 8:40am
use your log rules:

log (AB) = logA + logB

and

log (A/B) = logA - logB

1st one:

log_{3} [(x-5)(x+3)] = 2

by definition of logs

(x-5)(x+3) = 3^2 = 9

x^2 - 2x -24=0

(x-6)(x+4) = 0

x = 6 or x=-4 , but x=-4 would make log_{3}(x+3) undefined, so

x = 6

2nd:

log_{7}(x) + log_{7}(x-1) - log_{7}(2x) = 0

log_{7}[x(x-1)/(2x)] = 0

log_{7}[(x-1)/2] = 0

(x-1)/2 = 7^0

(x-1)/2 = 1

x-1=2

x = 3

## Answer this Question

## Related Questions

- Math - Solve the logarithmic equation. Express your solutions in exact form only...
- algebra - (2*log7 16)/(log3(√10+1)+log3(√10-1)log7 2
- ALGEBRA 1 - Lesson 3 Assignment .Explain the differences between solving these ...
- Algebra 1 - Lesson 3 Assignment .Explain the differences between solving these ...
- Math - (I have two questions) 1. Solve for x without a calculator: log3(x^2)=...
- Math - Express the following as a logarithm and simplify. 1. log(3x^2 + 11x - 20...
- Math - Express the following as a logarithm and simplify. 1. log(3x^2 + 11x - 20...
- Precalculus - Please help me with these questions ASAP!! Suppose that f(x)=log3...
- Math - logs - log_3(2x - 1) = 2, Find x. Here's what I've done: log_3(2x) * ...
- Math - Solve for x. log3(x+7)=2-log3(x-1) Write the exact answer using base-10 ...

More Related Questions