Question

How do you solve 27?

Answer 1

We have

$\left(\dfrac{2}{3}\right)^x=\dfrac{2^x}{3^x}$

And we want

$\dfrac{2^x}{3^x}=\dfrac{16}{81}=\dfrac{2^4}{3^4}$

Another way to read it is

$\dfrac{16}{81}=\left(\dfrac{2}{3}\right)^4=\left(\dfrac{2}{3}\right)^x$

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

Answer 2

Answer:

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

Step-by-step explanation: