Question

if 3^x=81 and 2^x+y=64, then x/y = ?

Answer 1

Recall the properties of exponents

If the $a^m=a^n,$ then $m=n$

Given: $3^x=81, 2^x^+^y=64$

Explanation:

Here write $81$ as the power of $3$

$81=3^4$

$\implies 3^x=3^4$

Since the base is the same, equate the exponents

$\implies x=4$     ........(1)

similarly, $64=2^6$

$\implies 2^x^+^y=2^6$

$\implies x+y=6$   ...........(2)

Solve equations (1) and (2)

$\implies x+y=6\\\implies 4+y=6\\\implies y=6-4\\\implies y=2$

Hence the value of $\frac{x}{y}=\frac{4}{2},$

$\implies \frac{x}{y}=2$

Answer 2

QUESTION:

If $3^x=81$ and $2^{x+y}=64$, then $\frac{x}{y} =?$

Given,

$3^x=81$ and $2^{x+y}=64$

To find,

$\frac{x}{y}$

Solution,

Here, it can be seen that the given problem is related to the exponents and powers.

The given equations are

$3^x=81$     ...(1)

$2^{x+y}=64$     ...(2)

Now, since $81=3^4$, so from eq. (1),

$3^x=3^4$

Thus, from the above equation, as bases are the same, the exponents must be equal, so we get,

x = 4.

From eq. (2),

$2^{x+y}=64$

Since $64=2^6$, so,

$2^{x+y}=2^6$

Again, the bases are the same. Hence, equating exponents,

$x+y = 6$

Earlier, as we've obtained x = 4. Substituting this value in the above equation,

$4+y = 6$

⇒ $y=6-4$

⇒ y = 2.

We have to determine $\frac{x}{y}$, substituting the above-obtained values of x and y, we get,

$\frac{x}{y}=\frac{4}{2}$

⇒ $\frac{x}{y}=2.$

Therefore, the value of $\frac{x}{y}=2$.