Posted by **mz deedee** on Friday, November 11, 2011 at 12:00pm.

solve the logarithmic equation . express solution in exact form

log5(x-9)+log5(x+4)=1+log5(x-5)

- precalculus -
**Steve**, Friday, November 11, 2011 at 12:30pm
1 = log5(5), so we have

log5(x-9)+log5(x+4)=log5(5)+log5(x-5)

log5[(x-9)(x+4)] = log5[5(x-5)]

raise 5 to the powers, and we have

(x-9)(x+4) = 5(x-5)

x^2 - 5x - 36 = 5x - 25

x^2 - 10x - 11 = 0

(x-11)(x+1) = 0

Solutions are 11,-1

However, -1 does not fit the original equation: log of negatives are undefined.

- precalculus -
**Reiny**, Friday, November 11, 2011 at 12:40pm
log5(x-9)+log5(x+4)=1+log5(x-5)

log5(x-9)+log5(x+4)=log5(5)+log5(x-5)

log5[(x-9)(x+4)] = log5[5(x-5)}

(x-9)(x+4) = 5(x-5)

x^2 - 5x - 36 = 5x - 25

x^2 - 10x - 9 = 0

x = (10 ± √136)/2 = appr. 10.83 or -.83

but for each of the above to defined, x > 9

so x = (10 + √136)/2 = 5 + √34

check my arithmetic

- Steve had right equation, precalculus -
**Reiny**, Friday, November 11, 2011 at 12:43pm
I have an error in my equation...

x^2 - 10x - 9 = 0 should be

x^2 - 10x - 11 - 0 , just like Steve had

then (x-11)(x+1) = 0

x = 11 or x = -1

so x = 11

## Answer this Question

## Related Questions

- Algebra 2 - Express as a logarithm of a single number or expression: 1. 5log4^p+...
- college algebra - solve the logarithmic equation. Please show all work. log5x+...
- Logarithm help - using logarithms to solve exponential equations. 5^1+x = 2^1-x...
- Algebra II - Log6(6^9)=??? Answer: 9 Ine^-3x=??? Answer: -3x Use log5(2) = 0....
- mathematics - Given that log5 3=0.683 and log5 7=1.209.without using calculator...
- Logs-Algebra - How do you graph the following logs? f(x)=log5 (x-2) f(x)=log5 x-...
- precalculus - log5 (x+3)= 1- log5 (X-1) where do I start?
- Algebra II - Use log5(2)=0.4307 and log5(3)=0.6826 to approximate the value of ...
- acc. alg 2 - exponentiating to solve equations: solve the eaquation, cheack for ...
- Math - My question says: Find the exact alue of x for which (4^x)*(5^[4x+3])=(10...

More Related Questions