Solve Equation for n where n is the power ($3^n = \frac{1}{81}$)

Question

I have the equation: $$3^n = \frac{1}{81}$$

And I need to find n. Can someone explain how I do this, with steps please (GCSE level)?

TIA.

Ok...can you write out the first few powers? $3^0,3^1,3^2,3^3, 3^4,\cdots$? — lulu, May 10 '16 at 17:56
GCSE. If $n$ is a positive integer then clearly there are no solutions. But if $n$ is a negative integer, say $n=-k$, then we have $3^n=\frac{1}{3^k}$. So we want a positive integer with $3^k=81$. So now follow lulu's hints. — almagest, May 10 '16 at 17:57
@MattCowley If you can't solve lulu's question, then your deficiencies won't be solved by asking stuff here. You need to ask someone to help you in person. — Git Gud, May 10 '16 at 17:58
If you dont know how to solve this I honestly think that it will be better try to learn about exponentiation at GCSE level, maybe through youtube vids or online courses. You can write $\frac1{81}=\frac1{3^4}=3^{-4}$ — Masacroso, May 10 '16 at 18:05

score 1 · Accepted Answer · answered May 10 '16 at 17:57

1

Use that $81 = 3^4$

Then $\frac{1}{3^4} = 3^n$

Then $n = -4$

answered May 10 '16 at 17:57

Luísa Borsato

score 0 · Answer 2 · answered May 10 '16 at 18:04

0

After doing some googling I learnt that

$$ b^y = x \therefore log_b(x) = y $$

So then

$$ 3^n = \frac{1}{81} \therefore log_3(\frac{1}{81}) = n = -4 $$

answered May 10 '16 at 18:04

Matt Cowley

2 Answers2