if x and y are numbers which have log_(2)(x)=4 and log_(2)(y)=5, find log2(xy^3)?

Answer 1

log_(2) (xy^3) = log_2 x + 3 log_2 y

= 4 + 3(5)
= 19

Answer 2

log_(2)(x) = 4
x = 2^4

log_(2)(y) = 5
y = 2^5

Plugging values of x and y>>
log2(xy^3)
= log2[(2^4)(2^5)^3]
= log2[2^4 . 2^15]
= log2[2^(4 + 15)]
= log2[2^19]
= 19

Answer 3

log(2)(xy^3) = log(2)x + log(2)y^3 = log(2)x + 3log(2)y

log(2)x + 3log(2)y = 4 + 3(5) = 4 + 15 = 19

log(2)(xy^3) = 19

Answer 4

log[base 2](x) = 4
log[base 2](y) = 5

x = 2^4 = 16
y = 2^5 = 32

log[base 2]{xy³} = log[base 2]{(2^4)(2^5)³} = 4 + 5*3 = 19

Answer 5

log(2) x = 4 so x=2^4
log(2) y = 5 so y=2^5


so
log(2) xy^3 becomes

log(2) (16 * 32^3) or log(2) (2^4 * (2^5)^3) or log(2) (2^4 * 2^15)

log(2) (2^19) = 19

i hope this helps

Answer 6

log[base 2](x) = 4
log[base 2](y) = 5

We want to find log[base 2](xy^3)

What we do is decompose this; these three log properties may be involved:
i) log[base b](ac) = log[base b](a) + log[base b](c)
ii) log[base b](a/c) = log[base b](a) - log[base b](c)
iii) log[base b](a^c) = c*log[base b](a)

log[base 2](xy^3)

Using log property (i):
log[base 2](x) + log[base 2](y^3)

Using log property (iii) on the second logarithm,

log[base 2](x) + 3log[base 2](y)

Now, we just substitute log[base 2](x) = 4 and log[base 2](y) = 5.

4 + 3(5) = 4 + 15 = 19