Practice using the log rules to add and subtract logarithms

Practice using the log rules to add and subtract logarithms

Rewriting expressions of the form $n\log(a)\pm m\log(b)$ as a single logarithm.

Rewriting $\log_{10}(x)$ in terms of $\log_{10}(a)$ and $\log_{10}(b)$, where $a$, $b$ and $x$ are given.

Calculating the amount of money in a savings account after a given amount of time, and calculating how long it will take for the amount of savings to exceed a given value. 

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Solving an equation of the form $a^x=b$ using logarithms to find $x$.

Finding $x$ from a logarithmic equation of the form $\log_ax = b$, where $a$ and $b$ are positive integers.

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The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Graphing $y=a\log_{b}(x)+c$

Graphing $y=a\log_{b}(\pm x+d)+c$

Simlify (expand) logarithmic expressions 

Using basic derivatives to calculate the gradient function of a hill $y=-e^x+b\ln\left(x\right)+c$, and then substituting values to find the gradient at specific distance from the sea. 

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. 

Differentiating the natural logarithm

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Differentiating the natural logarithm

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Differentiating the natural logarithm

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A portfolio of NUMBAS questions created for first year Natural Sciences students. The questions cover the topics: 

• Linear functions
• Quadratic functions
• Differentiation
• Integration
• Explonatial and logarithms 
• Further differentiation
• Further Integration
• Trigonometric Functions

Knowing the doubling time of a population and the population on day $t$, calculate the initial population and the number of days required for the population to reach a threshold. 

Calculating the rate of change of the temperature during a chemical reaction using the chain rule in a function of the form $T=ate^{-t}$, and finding the maximum temperature of the reaction.