I don’t understand question two (a) (i) in the 2019 algebra paper. How do I solve this?
Kia ora
this is a great question, which requires you to use “indices rules” to simplify it
Please let me know if you need any further clarification
regards
Mrs H
it says to leave your answers with positive indices though?
ok thank you, this does help a little bit, also I’m not sure how to convert an equation into logs
Hi Sarah
I have a couple of examples from last years Level 2 Algebra paper
firstly refer to the formula sheet
Question Three (a)(i)
this question uses the first log rule
as follows
Question Three (b)
I hope this helps Sarah
Please let me know if you need help with anything else
Nga mihi
Mrs H
@Sarah.Roycroft logarithms are often used to find a power, or exponent. For example:
From this equation you can just guess that x = 3. But what if you have, for example, the following equation:
It’s quite hard to use trial and error to find what x might be equal to. To find x, you first need to make x the subject of the equation, meaning that you will have x on one side of the equation and the rest on the other side. For that, we use logarithms, it’s basically just another way of writing the same equation:
If 
then 
As you see, base of your power becomes base of the logarithm, but now the power is the subject of the equation. Applying this formula to the question above we can express x as:
That is how you convert an equation into logs. You can then find x using a special table or your calculator. You could either convert the expression to an expression with only log base 10, by dividing log of the argument (1215) by log of the base (27). In this case you can just use the ‘log’ button on your calculator to find the answer. Note that when the base is not specified, that means the base is 10.
You could also use the logab() function. On a Casio fx-9750GII you need to press F4 (CALC) then F6 then F4. Enter the base first, then the argument. In this case you would enter logab(27,1215) which would give a result of 2.155. On a Casio fx-9860GIII you need to press F4 (MATH) then F2. Again you need to enter first the base, then the argument.
This answer means that 27 to the power of 2.155 is equal to 1215:
@Sarah.Roycroft if you provide specific examples that you struggle to solve we will be able to help you with them.
thank you for your detailed answer this really helped!
thank you for you detailed answer and examples with step by step solutions, this really helped!!
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