Desperate need maths help! how find subject y in terms of x: 3^y = 4(3^x-2) -1?

Answer 1

Your variable is an exponent, so you'll need logarithms. Where we go from here depends on how much you already know.

1) Assuming you're familiar with logs of various bases, log base 3 (which I will write as log[3]) is the best approach.

y = log[3](4(3^(x - 2)) - 1)

which can be rewritten multiple ways.

2) If you're only familiar with log base 10 (log[10]):

y = log[10](4(3^(x - 2))-1)/log[10]3

3) If you know the natural log (ln), you can use that, too: it'll be the same as answer 2, but with ln in place of log[10].

And, again, all of these can be broken down further, depending on what you know and what you want to do.

Upshot: Variable exponents use logarithms.

Answer 2

find the value of the answer on the right side of the equation (work amount in brackets first then multiply it by 4 and minus 1) so say if your answer is 18 then the left side of the equation must add up to 18 also. so if 3 was to the power of 2 (=9) then y would have to equal 18 divided 9 = 2. the formula can be written as y = (answer of the right side of the equation) divided by (number on the left^)