![]() If there are several logarithmic expressions, condense them. Then use the multiplication property from the prior video to convert. Then multiply through by log (3) to get log (x) 2log (3). Then replace both side with 10 raised to the power of each side, to get log (x)/log (3) 2. If it is a single logarithmic expression, expand it. Well, first you can use the property from this video to convert the left side, to get log ( log (x) / log (3) ) log (2). Calculators are not allowed for some questions.Īny space included in a number indicates a comma used to separate parating multiples of three digits from behind.Īny comma included in a number indicates a decimal point.ĭecimals are used appropriately rather than commasĬommas are used to separate digits appropriately. So, the questions are solved in a way that does not require a calculator.Īny question labeled WASCCE is a question for the WASCCE General MathematicsĪny question labeled WASSCE:FM is a question for the WASSCE Further Mathematics/Elective MathematicsĪll work is shown to satisfy (and actually exceed) the minimum for awarding method marks.Ĭalculators are allowed for some questions. ![]() There is no negative penalty for a wrong answer.Ĭalculators are not allowed. Please ensure you attempt all ACT questions. So, it is not just solving a question correctly, but solving it correctly on time. So, you should try to solve each question correctly and timely. Solved in less than a minute, to solve the questions that will take more than a minute. You use the time saved on those questions you Some questions will typically take more than a minute to solve. Some questions will typically take less than a minute a solve. This implies that you have to solve each question in one minute. The ACT is a timed exam.$60$ questions for $60$ minutes We expand and condense logarithms using the laws of logarithms and the laws of exponents. To Condense Logarithms is to write several logarithmic expressions as a single logarithmic expression. We can use the rules of logarithms we just learned to condense sums, differences, and products with the same base as a single logarithm. How to Condense/Expand Logarithms We can either compress a group of logs into a single log or expand a single log into a group of logs using the above rules of logs. We'll take on some gruesome expressions that involve logs and learn to write the expressions as a single logarithm.To Expand Logarithms is to write a single logarithmic expression as several logarithmic expressions. Expanding and Condensing Logarithms Condense each expression to a single logarithm. It's time to get back to mathematics and try simplifying logs using concrete formulas. Quite a few physical units are based on logarithms, for instance, the Richter scale, the pH scale, and the dB scale.Īlright, that should be enough of a description for now.Condense a logarithmic expression into one logarithm. Chemistry, e.g., the half-life decay and Expanding and Condensing Logarithms Learning Outcomes Expand a logarithm using a combination of logarithm rules.Medicine, e.g., the Quantitative Insulin Sensitivity Check Index (QUICKI).Statistics, e.g., the lognormal distribution.After all, whatever we raise to power 0 0 0, we get 1 1 1. Whatever the base, the logarithm of 1 1 1 is equal to 0 0 0. In other words, whenever we write log a b \log_a b lo g a b, we require b b b to be positive. ![]() The logarithm function is defined only for positive numbers. If you're curious, log base 2 calculator is the way to go. There is also the binary logarithm, i.e., log with base 2 2 2, but it's not as common as the first two. The former is denoted ln x \ln x ln x and its base is the Euler number - you can read more about it in the natural log calculator! The latter is denoted log x \log x lo g x with the base being (surprise, surprise!) the number 10 10 10. There are two very special cases of the logarithm which have unique notation: the natural logarithm and the logarithm with base 10 10 10. Before we learn how to rewrite logs, let's mention a few critical facts concerning them.
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