The two equations below are two different ways to say the same thing, but the first is an exponential equation, and the second is a logarithmic equation. 3 0 obj var date = ((now.getDate()<10) ? On to Solving Inequalities – you are ready!    Guidelines", Tutoring from Purplemath First, separate the factors with two different logs; then, move the 3 down and around to the front. If she deposits $2000 now, with interest compounded continuously, what interest rate will she need to get her down payment in time? We have to use the most accurate \(k\) we can, since logs are sensitive. Using the world population formula P = 6.9(1.011) t, where t is the number of years after 2011 and P is the world population in billions of people, estimate: a) the population in the year 2050 to the nearest hundred million, and . In about 8 days there will be 10,000 fleas.     = Note that we could have also take the log base 10 of both sides. (b) How many years will it take for the population to double? Write a logarithmic function in form \(y=a\log \left( {x-h} \right)+k\) from a graph (given asymptote and two points). (b) We’ll use the same formula, but now we need to use logs to get the variable in the exponent down. The juice is Word Problems (page We solved a half-life problem above in the Exponents section, but if you need to find a time (a variable in the exponent), then you need to use logs. Yikes! requiring, among other things, that the student first generate the exponential √, \(\displaystyle \begin{array}{c}{{e}^{{.004x}}}=7\\\cancel{{\ln }}{{\cancel{e}}^{{.004x}}}=\ln \left( 7 \right)\,\,;\,\,\,\,.004x=\ln \left( 7 \right)\end{array}\), \(\displaystyle x=\frac{{\ln \left( 7 \right)}}{{.004}}\,\,\approx \,\,486.48\). We will get the same answer.). As we know, in our maths book of 9th-10th class, there is a chapter named LOGARITHM is a very interesting chapter and its questions are some types that are required techniques to solve.