Question

Hi i just need a simple explanation for this question!

Answer 1

Answer:

x = $\frac{5}{3}$

Step-by-step explanation:

$3^{5} = 27^{x}$

These problems are getting you ready to work with exponential functions,

and ultimately with logarithms. The point here is that with variable exponents (notice the exponent is an x (on the right one) and not a number. Variable exponents can not be solved with regular algebra "rules" you need new ones.

The new ones will be Logs....

For now (until you learn logs) , you have to use some "tricks"

the "trick" in this problem is that you have to realize that 27 = $3^{3}$...

with "common bases" this problem becomes trivial

$3^{5} =(3^{3} ) ^{x}$

so now the bases are the same and the equals sign suggests that

3x = 5

thus x = $\frac{5}{3}$

Answer 2

Answer:

5/3

Step-by-step explanation:

3^5 = 27 ^x

Rewrite 27 and 3^3

3^5 = 3^3^x

We know that a^b^c = a^(b*c)

3^5 = 3^(3x)

The bases are the same so the exponents are the same

5 = 3x

Divide by 3

5/3 =x