# population word problems logarithmic

Why do we need to do all this? = log[0.0003] = 3.52287874528... ...which is less than = (2.5 ×1013)I0, Population Growth Problem. I have to admit that logs are one of my favorite topics in math. In 2003, the population of the state of New York was 10.78 million people. A large colony of fleas is growing exponentially on the family dog (yuck!). <> Chapter 12_Logarithms Word Problems Make a note that doubling or tripling time is independent of the principal. Take the ln of both sides; we can use ln since we we’re not dealing with base 10. Logarithmic word problems, Here’s a practical example where we can use logs to solve the algebraic equation $$250=100{{\left( {1.05} \right)}^{t}}$$ to get the number of years, $$t$$, that it would take to go from $100 to$250 with a yearly interest rate of 5%. decibels. These are horizontal transformations or translations. Find the pH value and determine whether the juice is basic or acidic. Remember again that everything on top has a plus before it, and everything on bottom has a minus before it. We could also solve this using the matching base method, as we did in the previous problem. Yikes! of exercises involves exponential equations.... Top Genius! Take the natural log (ln) of both sides. Using the graphing calculator, put use the logs in $${{Y}_{1}}$$ and $${{Y}_{2}}$$ using LOGBASE (MATH A or ALPHA, WINDOW 5). Since the whole term is raised to 4, first move the 4 down around to the front. b) You test In other words, my rifle √, $$\displaystyle \begin{array}{c}{{e}^{{.004x}}}=7\\\cancel{{\ln }}{{\cancel{e}}^{{.004x}}}=\ln \left( 7 \right)\,\,;\,\,\,\,.004x=\ln \left( 7 \right)\end{array}$$, $$\displaystyle x=\frac{{\ln \left( 7 \right)}}{{.004}}\,\,\approx \,\,486.48$$. Solution: First divide by 5 to get $${{e}^{{.004x}}}$$ by itself. We typically use ln instead of log, unless we’re dealing with base 10. In the previous problem, notice that the principal was not given and also notice that the P cancelled. Then separate the factors, and finally push through the 4. or 3.5, 2. The population is expected to grow by the function $$p\left( … Remember to check your answers to make sure you don’t have a negative log argument. Learn this well! So when you take the log of something, you are getting back an exponent. We learned how to put exponents in the calculator (using ^) here in the Exponents and Radicals in Algebra section. Use the loop to get the variable out of the log argument. Write an equation to describe the logarithmic function in form \(y=a{{\log }_{b}}x$$, with a given base and a given point. (Note: for $$y={{\log }_{3}}\left( {2\left( {x-1} \right)} \right)-1$$, for example, the $$x$$ values for the parent function would be $$\displaystyle \frac{1}{3},\,\,1,\,\,\text{and}\,\,3$$. You can check your answer in the calculator by verifying that $$100{{\left( {1.05} \right)}^{{18.78}}}\approx 250$$. We have a positive log argument, so it works. accessdate = date + " " + From counting through calculus, making math make sense! Let’s do some problems and see what techniques we use: \begin{align}2{{n}^{2}}+10&=22-5n\\2{{n}^{2}}+5n-12&=0\\\left( {2n-3} \right)\left( {n+4} \right)&=0\\n=\frac{3}{2},\,\,\,\,n=-4\end{align}. Madison really wants to buy a car. It’s almost like the 2’s cancel out. endobj just a big truck going too fast over the speed humps in my neighborhood. 4. Here are some simple log problems where we have to use what we know about exponents to find the log back. (b)  How many years will it take for the population to double? Available .22 rimfire at a given point, and solving for a given variable; they're pretty straightforward. We also needed to simplify the $${{\log }_{2}}4$$ to 2 $$({{2}^{2}}=4)$$. In about 4.56 years, there will be less than 300 students. $$\displaystyle \begin{array}{l}\log x+\log {{\left( {1-x} \right)}^{{\frac{1}{2}}}}-\log {{\left( {x+1} \right)}^{4}}\,\,\,\\\,\,\,\,\,=\,\,\,\log \left[ {\frac{{x\sqrt{{1-x}}}}{{{{{\left( {x+1} \right)}}^{4}}}}} \right]\end{array}$$. There are 400 fleas initially. \begin{align}A&=P{{e}^{{rt}}}\\2500&=2000{{e}^{{r(4)}}}\\1.25&={{e}^{{4r}}}\\\ln \left( {1.25} \right)&={{\cancel{{\ln e}}}^{{4r}}}\\t&=\frac{{\ln \left( {1.25} \right)}}{4}\approx .056\\&\approx 5.6\%\end{align}. (fourdigityear(now.getYear())); should you follow the rules and wear ear protection when relaxing at Problem 6: Town A had a population of 10,000 in 1900 and 20,000 in 1950. There are basically two formulas used for exponential growth and decay, and when we need to solve for any variables in the exponents, we’ll use logs. Typically (and unless otherwise stated), $$t$$ represents the number of years after the first year, in our case, 2009. We have to also remember that if the function shifts, this “anchor point” will move. There are, Also note that sometimes you are given the equation, for half-life or any decay problems, and then the $$k$$.    Guidelines", Tutoring from Purplemath To make sure we keep the inequality signs in the correct place, I found it easiest to raise both sides to the log base, which is 2.