Posted by **Kenya** on Saturday, April 30, 2011 at 11:08pm.

Solve the equation.

2log3 y = log3 4+ log3 (y+8)

Here's what ive got

take out the logs and say y^2= 4+ y +8

which simplifies to (y^2)-y=12

how do i simplfy the y?

- Algebra -
**Jai**, Sunday, May 1, 2011 at 1:21am
note that you cannot simplify the right side equation log3 (4) + log3 (y+8) , by 4 + y + 8 ... they should be multiplied. recall some laws of exponents; if we are add terms of the same base, for example

log 3 + log 5

this simplifies to

log(3*5) or log 15

going back to the problem, the equation simplifies to

2log3 y = log3 4 + log3 (y+8)

log3 (y^2) = log3 (4*(y+8))

log3 (y^2) = log3 (4y + 32)

cancelling out the log3,

y^2 = 4y + 32

y^2 - 4y - 32 = 0

this is a quadratic equation. since it's factorable, let's just factor this one:

(y - 8)(y + 4) = 0

y = 8 and y = -4

note that y = -4 is extraneous, since if we substitute this back to the original, and take its log:

left side: 2log3 (-4) = undefined

thus,

y = 8

hope this helps~ :)

- Algebra -
**Anonymous**, Sunday, May 1, 2011 at 10:45am
Jai, your a life saver! you explained everything perfectly! thank you sooo much!

that helped a ton, thanks! : )

## Answer This Question

## Related Questions

- Math - (I have two questions) 1. Solve for x without a calculator: log3(x^2)=...
- Algebra (logs) - Please help, I need help on these two problems. Solve the ...
- Math - logs - log_3(2x - 1) = 2, Find x. Here's what I've done: log_3(2x) * ...
- Math - Solve the logarithmic equation. Express your solutions in exact form only...
- ALGEBRA 1 - Lesson 3 Assignment .Explain the differences between solving these ...
- Algebra 1 - Lesson 3 Assignment .Explain the differences between solving these ...
- Pre-Cal - 1) Solve the equation exactly for x: log3 x - log3(x-3) = 2 I got 1 as...
- Math - Logarithms 3^x-2=18 Work log(3^x-2)=log18 (x-2)log3=log18 xlog3-2log3=...
- Precalculus - Please help me with these questions ASAP!! Suppose that f(x)=log3...
- Calculus - Find the inverse of each relation: y = (0.5)^(x+2) and y = 3log base ...

More Related Questions