If 4log2a=6log2b=3plog2c and also a3b2c=1, then the value of p is equal to

4log2a =6log2b =3plog2c =xlog2a =4x⇒ a=24xlog2b =6x⇒ b=26xlog2c =3px⇒c=23pxa3 b2c=1212x⋅212x⋅23px=20224x+3px=20∴24x+3px=0∴3px=−24x∴p=−8

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If {_{2}a}{4} = {_{2}b}{6} = {_{2}c}{3p} and also a^{3}b^{2}c

Question

If $\frac{lo g _{2} a}{4} = \frac{lo g _{2} b}{6} = \frac{lo g _{2} c}{3 p}$ and also $a^{3} b^{2} c = 1$ , then the value of $p$ is equal to

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William Discussed

\frac{lo g _{2} a}{4} = \frac{lo g _{2} b}{6} = \frac{lo g _{2} c}{3 p}

and also

a^{3} b^{2} c = 1

, then the value of

p

is equal to

10 mins ago

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10 mins ago

\frac{lo g _{2} a}{4} = \frac{lo g _{2} b}{6} = \frac{lo g _{2} c}{3 p} = x lo g_{2} a = 4 x

\Rightarrow a = 2^{4 x}

lo g_{2} b = 6 x

\Rightarrow b = 2^{6 x}

lo g_{2} c = 3 p x

\Rightarrow c = 2^{3 p x}

a^{3} b^{2} c = 1

2^{12 x} \cdot 2^{12 x} \cdot 2^{3 p x} = 2^{0}

2^{24 x + 3 p x} = 2^{0}

∴ 24 x + 3 p x = 0

∴ 3 p x = - 24 x

∴ p = - 8

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Question Text	If $\frac{lo g _{2} a}{4} = \frac{lo g _{2} b}{6} = \frac{lo g _{2} c}{3 p}$ and also $a^{3} b^{2} c = 1$ , then the value of $p$ is equal to
Answer Type	Text solution:1
Upvotes	150