TMUA Logarithms
Knowledge of how to manipulate logarithms using the various log rules, as well as drawing sketches of log graphs, knowing the range and domain of logs, how to switch between logs and exponents, how to solve exponential equations with logs, and how to disentangle such exotic animals as logarithmic simultaneous equations, is absolutely essential for TMUA success.
For those so interested, we offer both one to one TMUA coaching on Logarithms, as well as online group coaching via Zoom - 'TMUA Prerequisite Maths One' is Session #1 of 20 and covers the basic rules, and 'TMUA Exponents and Logarithms' is Session #3 of 20 and covers what needs knowing for TMUA success. Check our TMUA Group Coaching Schedule page for dates when these sessions are available - details of what we cover in each group session can be found on our TMUA Coaching Sessions Overview page. For more general information on our online sessions check out our 'Online Coaching FAQ'.
Feel free to contact us if you require more information regarding any of the above.
Free Revision Resources
The below list of questions links to short videos (teasers) on our YouTube channel which directly or indirectly test elements of what is required to succeed in answering TMUA questions on logarithms - they also provide a detailed solution to the question posed, together with tips and tricks and are arranged roughly in increasing order of difficulty. All the videos are taken from the Gresty Academy YouTube podcast 'A Crash Course in TMUA Must Know Maths' which contains hundreds of TMUA style questions and is great for revision.
- Teaser #212 - tests how to find number of real solutions of x^2-ln(x)-4=0 - Standard
- Teaser #174 - tests ability to solve an exponential equation using manipulation - Standard
- Teaser #13 - tests understanding of changing log base from 3.5 and simplifying - Standard
- Teaser #493 - tests understanding of the various components of logarithms and exponents and their allowed values - Standard
- Teaser #488 - tests understanding of log bases and their respective graphs - Medium
- Teaser #472 - tests ability to solve a trio of log equations with unknown bases - Medium
- Teaser #453 - tests how to solve inequalities to find maximum of logs with bases more and less than 1 - Medium
- Teaser #442 - tests understanding of manipulating logs to base less than one - Medium
- Weekend Workout #9 - tests how to solve an exponential equation of form a^x=b^y using 'change of base of exponents' producing a log result- Medium
- Teaser #126 - tests how to find the equation of the gradient of a fairly complex function involving logs at the origin - Medium
- Teaser #12 - tests ability to find domain of a log of a polynomial - Medium
- Teaser #414 - tests manipulation of logs and then recognising coprime numbers - Medium
- Teaser #272 - tests knowledge of domains of both logs and square roots - Medium
- Teaser #90 - tests understanding of compound interest calculations - (the calculation itself is beyond TMUA) - Medium
- Teaser #29 - tests ability to manipulate log(log(log(x))) - Medium
- Teaser #137 - tests ability to manipulate a tricky log expression - Medium
- Teaser #79 - tests ability to arrange graphs according to their gradient at a point - Medium
- Teaser #426 - tests understanding of how to solve an exponential equation with x being a power of a power of a power - Medium
- Teaser #427 - tests ability to arrange various expressions in increasing order by clever approximations - Medium
- Weekend Workout #10 - tests knowledge of using a^(log(a)b)=b to simplify a log/exponent equation - Quite Tough
- Teaser #198 - tests ability to simplify ln(ln(x))=e - Quite Tough
- Teaser #504 - tests advanced manipulation of two log(log) functions to solve an inequality - Quite Tough
- Weekend Workout #4 - tests knowledge that e^(ln(a))=a - Quite Tough
- Teaser #298 - tests ability to differentiate ln(x) and find a common tangent with a cubic- Quite Tough
- Teaser #491 - tests understanding of all steps required to correctly solve a log = log equation - Tough
TMUA Past Questions involving Logarithms: SP p1 q5; SP p1 q8; SP p1 q11; SP p1 q14; SP p2 q5; SP p2 q10; SP p2 q11; 2016 p1 q11; 2016 p1 q16; 2016 p2 q7; 2017 p1 q14; 2017 p2 q8; 2017 p2 q18; 2018 p1 q14; 2018 p1 q15; 2019 p1 q11; 2019 p1 q15; 2019 p2 q15; 2020 p1 q15; 2021 p1 q10; 2021 p1 q20; 2021 p2 q14; 2021 p2 q17; 2022 p1 q6; 2022 p1 q11; 2022 p2 q15; 2023 p1 q7; 2023 p2 q6
Practice makes perfect - good luck in your studies!