Solving Exponential Equations We use the inverse properties to solve both exponential and logarithmic equations: In particular, to solve exponential equations that don't have the same base on both sides of the equal sign, take logs of both sides.
Posted on September 5, by David Sellers I realized something the other day while doing a curve fit in Excel that I figured was worth sharing. It could be pretty tempting to write a formula that used the trend line equation and assume it was correct.
And technically, it is correct. But, in some cases, especially with high power polynomials, your predictions could be way off if you did that because of the compounding of rounding errors.
In other words, the coefficients presented in the equation are correct, but rounded off. And for some applications, the digits that were dropped could make the difference between making an accurate prediction from your data and one that was not so good, especially if you multiply them by numbers that have big exponents.
Most of you probably already realize this, and when I noticed the issue, I sort of had a hunch about the reason for it. But in figuring out how to work around it, I learned some things that will probably be useful, so I thought I would share them.
How I got into this was that I was working on a control valve selection for a condenser water system that has a number of different operating flow rates. So, I was looking at the valve performance for my selection at different flow rates.
I was basing my selection of a Bray series 30 butterfly valve and had the data for its flow coefficient a. Plus, I guess I got a little curious. So, I plotted my curve and got this as a result. Visually, the trend line looked like a pretty good fit with the 5thorder polynomial. So, I then wrote a formula using the coefficients in the trend line equation and got this result when I plotted it to check myself.
As you can see, quite a difference. Initially, of course, I thought I had miss-entered one of the coefficients. But when that did not prove to be the case, I realized that with the high power polynomials x to the 5thfor instance even small change in the coefficient would make a big change in the result and that the problem was probably related to the rounding off of the coefficients.
That got me curious about how you would actually get more accurate numbers for the coefficients out of Excel.
My reasoning was that Excel must know them; otherwise it could not have drawn the trend line that visually showed a much closer fit. In general terms, it is a least squares curve fitting technique where you input your y and x values and the function returns the coefficients for the equation for your line.
It can also force the y intercept to be zero and give you all of the statistical data about the line like the r2values, etc. It is one of the statistical functions, and when I read through the discussion at the Excel tutorial link I reference above, I was a bit overwhelmed by the math jargon.
Plus, it was not clear to me how to apply it for the valve CVsituation. I would have never figured it out from the Excel tutorial information. In addition to showing how to apply LINEST for a polynomial, the article also shows how to apply it for other data fits including logarithmic, powers, and exponentials.When you're solving logarithmic equations, rewrite it first in its exponential form.
See how it's done with our video instructions then try it yourself. Evaluating logarithms without a calculator. 4. Common logarithms.
5. Natural log: ln. 6. Solving logarithmic equations. Graphing logarithmic . Free exponential equation calculator - solve exponential equations step-by-step. Whether you're trying to get a grade to be proud of on that next algebra test, helping students better understand mathematical problems in the classroom or designing a blueprint for a mechanical device, finding the right graphing calculator can help.
Solving Log Equations with Exponentials. Note that the base in both the exponential form of the equation and the logarithmic form of the equation is "b", you can see that it does work. (Try it on your calculator, if you haven't already, so you're sure you know which keys to punch, and in which order.).
The trick to solving a problem like this is to rewrite the number and you have a calculator that can only compute logarithms in base Your calculator can still help you with log3 (7) because the change of base formula Now divide the equation above by logb (a), and we’re left with the change of .
evaluate exponential and logarithmic expressions without a calculator. [IS.4 - Struggling Learners] Logarithmic equation: An equation in the form of y=logax, “We can rewrite the expression as 3 = log 2 8.
3 is the logarithm, base 2, of 8.