solving for y in terms of x

**mxhockey140** · December 15th 2008, 03:19 PM

i dont know how to go about this problem, solve the following for y in terms of x: 10^y=5^x-3
thank you!

**Chris L T521** · December 15th 2008, 03:43 PM

Originally Posted by mxhockey140

i dont know how to go about this problem, solve the following for y in terms of x: 10^y=5^x-3
thank you!

Before I proceed, is it $10^y=5^{x-3}$ or $10^y=5^x-3$ ?

**mxhockey140** · December 15th 2008, 03:46 PM

its the first one x-3 is the exponent

**Chris L T521** · December 15th 2008, 03:49 PM

Originally Posted by mxhockey140

its the first one x-3 is the exponent

The way to do this involves taking the natural log of both sides:

$10^y=5^{x-3}\implies \ln\left(10^y\right)=\ln\left(5^{x-3}\right)$

Using power rules, we can rewrite this as $y\ln\left(10\right)=\left(x-3\right)\ln\left(5\right)$

Can you take it from here?

**mxhockey140** · December 15th 2008, 04:07 PM

no not really.. im not the best with this stuff.

**mr fantastic** · December 15th 2008, 04:09 PM

Originally Posted by mxhockey140

no not really.. im not the best with this stuff.

If you're attempting questions involving exponentials and logarithms it's expected that you can make y the subject by solving what is essentially a linear equation.

Can you solve $a y = b (x - 3)$ for y?

**mxhockey140** · December 15th 2008, 05:14 PM

thats why i was looking for help..

**mr fantastic** · December 15th 2008, 07:47 PM

Originally Posted by mxhockey140

thats why i was looking for help..

I would have assumed that you were looking for help in getting from the original equation to a stage where you could reasonably be expected to complete the solution.

Since another question you've asked (http://www.mathhelpforum.com/math-he...28-curves.html) strongly suggest that you're studying calculus, your trouble in solving a linear equation is surprising and of concern.

I ask again:

Can you solve

for y?

What about solving $3y = 4(x - 3)$ for y?

If you cannot at least do this last one then I would suggest that your real problem is an insufficient grasp of the mathematical knowledge prerequisite to the topic you're currently being taught. In which case you're strongly advised to go back and revise that material in collaboration with your instructor.

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