# Homework Help: Solving an equation for y

1. Apr 7, 2010

### steve snash

1. The problem statement, all variables and given/known data
solve the equation for y,
log5 (14y-12)=2x^6-13

3. The attempt at a solution
ive got no idea how to work it out im guessing it must be something to do with making the left side with y equal 1, log5 5 =1 but how do i get that?

2. Apr 7, 2010

### Staff: Mentor

Every log equation can be written as an equivalent exponential equation, and that's what you want to do here.

The basic idea is that M = logaN <==> N = aM

3. Apr 7, 2010

### lanedance

it may help by re-writing the log base b as:
$$log_b(z) = \frac{ln(z)}{ln(b)}$$

4. Apr 7, 2010

### Staff: Mentor

Or maybe not. The OP would like to solve for y, which means he needs to get rid of the log part, not write it in some other base.

5. Apr 7, 2010

### lanedance

fair point - i was heading in the same direction, i've just found a lot of people find it easier convert:
X = lnY <==> Y = eM
rather than
M = logaN <==> N = aM
though i know it is really just a redundant step

6. Apr 8, 2010

### steve snash

that makes the equation come up as (14y-12)=5^(2x^6-13)
this then becomes ,
y=(5^(2x^6-13)+12)/14
which i found is the wrong answer =(
is there a way to get rid of the 5^ and simplify it down???

7. Apr 8, 2010

### HallsofIvy

What do you mean "found is the wrong answer"? That is a perfectly good solution to the problem.

8. Apr 8, 2010

### steve snash

really, sweet ty hallsofivy