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C2 log question...

Solve the simultaneous equations:
Log2(x)+Log8(y)=-1
Log4(x)+Log2(y)=2

All logs here are to the base, ie not Log 2x
Please help :frown:

Reply 1

JJMills

Before I go into it, have you got a value of x and y so I can check I'm right?

Edit:

I managed to get an answer that works for both of your values. Pretty sure I've never done anything like this for C2 though, what exam board are you with? Also, how many marks was this question?

To do this question you need to use pretty much all the rules for logs you know. Using

log_a x = \frac {log_b x}{log_b a}

to give them all the same base and

b*log_a x = log_a x^b

log_a x + log_a y = log_a xy

and

log_a x - log_a y = log_a \frac {x}{y}

to simplify the equations.

I'd advise you have another got at this before you look at my workings. Make sure you put them all in the same base for ease and then manipulate the equations to get values for x and y.

Spoiler

(edited 11 years ago)

Reply 2