Let log _a b=4, log _c d=2, where a, b, c, d | vedclass

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Question

(a)

We have, $\log _a b=4$, $\log _c d=2, a, b, c, d \in N$

$\Rightarrow b=a^4, d=c^2$

$\Rightarrow b-d=7=a^4-c^2$

$\Rightarrow 7=\left(a^

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Vedclass · Answer

(a)

We have, $\log _a b=4$, $\log _c d=2, a, b, c, d \in N$

$\Rightarrow b=a^4, d=c^2$

$\Rightarrow b-d=7=a^4-c^2$

$\Rightarrow 7=\left(a^2+cight)\left(a^2-cight)$

$\Rightarrow 7 	imes 1=\left(a^2+cight)\left(a^2-cight)$

$	herefore a^2+c=7 	ext { and } a^2-c=1$

$	ext { On solving, we get } a=2 	ext { and } c=3$

$	herefore c-a=3-2=1$

Let $\log _a b=4, \log _c d=2$, where $a, b, c, d$ are natural numbers. Given that $b-d=7$, the value of $c-a$ is

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