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I have seen people look at log (several digit number) and rattle off the first couple of digits. Is Trigonometry Harder Than Precalculus – Know The Myth. where m is a number between 1 and 10 and n is an integer (a whole number). Log2 is a growing function, so if a < x < b, log(a) < log(x) < log(b) (for all bases bigger than 1, including 2) Log (a*b) = Log(a) + Log(b). A logarithm is defined as the power or exponent to which a number must be raised to derive a certain number. The solution of any logarithm is the power or exponent to which the base must be raised to reach the number mentioned in the parenthesis. A: Because HNO3 is a strong acid, [H+] = 4.2 x 10-3 M.  The pH of a solution is equal to the negative log of the concentration. 0 $2\log_2 3 \cdot\log_3 2$ without using a calculator Required fields are marked *. So the approximate value of the Ka is 3.8 x 10-4 M, which is closest to answer c). To find z, first let us convert this to exponential form: 121z = 11 Is this a typo...? Q: The K a of an acid whose buffer has a pH of 3.62 in a solution containing equal M of acid and conjugate base is closest to: $\begingroup$ If you know the log of a few prime numbers, you can find the log of a number that is close to the desired one. Example: log 1000. In such cases, it is understood that the base value by default is 10. One of the most important principles of mastering MCAT math is remembering that you don’t have to calculate the exact answer to every problem, you just need to get close enough to select the correct answer from the list of possible choices. In this case, pH = –log(4.2 x 10-3). Log Base 2. 2z = (25)1/2 4z = (1/43) We know that 25 = 32 Solving a logarithm without a calculation is easier than it might seem. 2z = (25/2) The Log Base 2 Calculator is used to calculate the log base 2 of a number x, which is generally written as lb(x) or log 2 (x). Let’s see how a logarithm is depicted: c times greater than the [H+] of the other. However, a 1M difference in [H+] isn’t really meaningful. Logarithms are one of the most difficult math topics on the MCAT because many of us haven’t studied them since high school and probably never learned how to solve them without a calculator. log 2 (32) = log 2 (25) = 5 Feel free to contact me if you have any query. So how exactly does this work? Recall that pH is the negative log of the [H+]. For example, 10X = 100. However, we are trying to solve for the Ka, not the pKa (recall also that pKa = –log(Ka) ), and we will need to use the approximation we learned before but in reverse. log 2 (32) = log 2 (25) = 5 log 6 (1) = log 6 (60) = 0 log 4 (16) = log 4 (42) = 2. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. It may not display this or other websites correctly. The log function is used to solve equations where the variable is an exponent with base 10. That's a log with base 2, log2. log 4 (16) = log 4 (42) = 2. If xz = y, then ‘z’ is the answer to the log of y with base x, i.e., log x (y) = z We can rewrite the pH of 3.62 as 4 – 0.38, putting it in the form n – 0.m shown above. In chemistry, acidity can be measured on a linear scale from [H+] = 0.00000000000001M to [H+] = 1M. Hi, I am Matt E Gordon. Or do you have any questions for us? Make sure to check out the rest of the MCAT Tips and Tricks Series: JavaScript is disabled. In such cases, it is understood that the base value by default is 10. This equation is not as difficult as it may seem. The pH of a solution is equal to the negative log of the concentration. Now to calculate log base 2, you can use any of these two, just that you will need to convert it into base 2. One the base and the number in the parenthesis are identical, the exponent of the number is the solution to the logarithm.