Log maths Q?? If log(base2)y = 3 + log(base2)x, give an expression for y in terms of x with no logarithms

the answer was y = 8x

please help ! so confused

log2(y) = 3 + log2(x)

First, subtract log2(x) from each side:

log2(y) - log2(x) = 3

Combine the logarithmic terms:

log2(y/x) = 3

Raise 2 to the power of each side to cancel out the logarithm:

y/x = 2^3

y/x = 8

Now, multiply each side by x:

y = 8x

the notation I have used is logm(n), which is the logarithm (of base m) of n

log2(y) = 3 + log2(x)
log2(y) = 3log2(2) + log2(x)

because loga(a) = 1, therefore 3 = 3log2(2) [LOG LAWS]

log2(y) = log2(2^3) + log2(x)

because logc(a^b) = blogc(a) [LOG LAWS]

log2(y) = log2(8) + log2(x)
log2(y) = log2(8x)

because logc(ab) = logc(a) + logc(b) [LOG LAWS]

log2(y) = log2(8x)

2^(log2(y)) = 2^(log2(8x))
y = 8x

because c^(logc(a)) = a [LOG LAWS]