Question

How do you solve 27?

Answer 1

16 / 81 = 0.1975308642

2 / 3 = .6666666666666

.6666666666666^x = 0.1975308642

Taking logs of both sides:

x * log (.6666666666) = log (0.1975308642)

x = log (0.1975308642) / log (.6666666666)

x = -0.7043650362 / -0.1760912591

x = 4

Explanation:

Answer 2

We have

`\left((2)/(3)\right)^x=(2^x)/(3^x)`

And we want

`(2^x)/(3^x)=(16)/(81)=(2^4)/(3^4)`

Another way to read it is

`(16)/(81)=\left((2)/(3)\right)^4=\left((2)/(3)\right)^x`

It should be clear that the solution is
`x=4`