i need help solving for log2(24) thats a base of 2. Im given that log2(3)=1.585 and log2(5)=2.322?

Question

can anyone help me solve this?

Answer 1

24 = 2^3 * 3
log24 = 3log2 + log 3
log2 to the base 2 is 1
log24 = 3*1 + 1.585
= 4.585

Answer 2

log2(3 x 2 x2 x 2) = log2 (3) + log2 (2^3)

= log2 (3) + 3log2 (2)

= 1.585 + 3(1) , Since log2(3) = 1.585 and log2(2) = 1

Hence log2 (24) = 4.585

Answer 3

log2(2*12)
log2(2) + log2(12
1 + log2(3*4)
1 + log2(3) + log2(4)
1 + 1.585 + log2(2*2)
1 + 1.585 + log2(2) + log2(2)
1 + 1.585 + 1 + 1
=
4.585

Answer 4

= log2(24)
= log2(2^3 * 3)
= log2(2^3) + log2(3)
= 3log2(2) + log2(3)
= 3(1) + 1.585
= 3 + 1.585
= 4.585

Answer 5

if you have

logy(x) = z log base y of x equals z

then take

y^(logy(x)) = y^z but y^(logy(x)) = x

x = y^z then take log base 10 or e (loge(x) = ln(x))

so

log10(x) = log10(y^z) = z*log10(y)

so you can convert logarithms to base 10 or e (both of which your calculator should have)

so z=log10(x)/log10(y)
so

log2(24) = log10(24)/log10(2) = 4.585

you can do the problem above also by 'cheating'

log2(24) = log2(8*3) = log2(8) + log2(3) = 3 + log2(3) = 4.585 without using a calculator, given the value of log2(3) you gave...

Answer 6

log(base 2)(24)
= log(base 2)(3 * 8)
= log(base 2)(3 * 2^3)
= log(base 2)(3) + log(base 2)(2^3)
= log(base 2)(3) + 3log(base 2)(2)
= 1.585 + 3*1
= 4.585.

You do not need log(base 2)(5) for this question.

Answer 7

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Answer 8

gudspelling is right. the log[2] 5 is irrelevant.