Given that 2log y = 8log p + 4log q, Express y in terms of p & q?

Cunnyguy

2 years ago

Given that 2log y = 8log p + 4log q, Express y in terms of p & q?
Answer 👇
y = p⁴q²

All_for_one

2 years ago

To express y in terms of p and q from the equation 2log(y) = 8log(p) + 4log(q), you can use logarithm properties to simplify it:

2log(y) = 8log(p) + 4log(q)

Using the properties of logarithms, you can rewrite this equation as:

log(y^2) = log(p^8) + log(q^4)

Now, apply the property of logarithms that states log(a) + log(b) = log(ab):

log(y^2) = log(p^8 * q^4)

Since the logarithms are equal, their arguments must also be equal:

y^2 = p^8 * q^4

Now, to express y in terms of p and q, take the square root of both sides:

y = √(p^8 * q^4)

y = p^4 * q^2

So, y is expressed in terms of p and q as y = p^4 * q^2.

Faheemadeiza2012

2 years ago

To express y in terms of p and q using the equation 2log(y) = 8log(p) + 4log(q), you can use logarithmic properties. Start by dividing both sides of the equation by 2:

log(y) = (8/2)log(p) + (4/2)log(q)

This simplifies to:

log(y) = 4log(p) + 2log(q)

Now, you can use the properties of logarithms to combine the logs on the right side of the equation:

log(y) = log(p^4) + log(q^2)

Using the properties of logarithms, you can combine these logs into a single log:

log(y) = log(p^4 * q^2)

Now, since the logarithms are equal, the quantities inside the logs must also be equal:

y = p^4 * q^2

So, y is expressed in terms of p and q as:

y = p^4 * q^2