Question

log b base a =3/2 log d base c = 5/4 if a-c= 9 then b-d =?

Answer 1

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Answer 2

Answer:

$b-d=125-32=93$

Step-by-step explanation:

$log_{a}b=\frac{3}{2}$ and $log_{c}d=\frac{5}{4}$

Let, $a^{\frac{1}{2}}=p$ and $c^{\frac{1}{4}}=q$, then

$b=p^{3}$ and $d=q^{5}$

It is given that a-c=9, ⇒$p^{2}-q^{4}=9$

⇒$(p-q^{2})(p+q^{2})=9$

Since, 9 can be expressed as 3×3, then $(p-q^{2})=(p+q^{2})$ which is not possible.Therefore, $p-q^{2}=1$ and $p+q^{2}=9$

Adding both the equations,

$p=5$ and $q=2$ (Since, we take positive value)

Therefore, $b=5^{3}=125$ and $d=2^{5}=32$

Hence, $b-d=125-32=93$