Question

Please answer this question correct, no wrong answers please!​

Answer 1

Answer:

Q(10):- Ans is 5

Step-by-step explanation:

6^3=216

i,e. x=3.

put x in second EQ it gives ans 5^(9-8)

i,e. 5^(1)= 5 itself.

Answer 2

Answer:

$\mathrm{Q10.\ 5}$

$\mathrm{Q11.\ \bigg(\dfrac{81}{256}\bigg)}$

Step-by-step explanation:

Given Questions :

$\text{Q10. 6^x = 216, then find the value of 5^{3x-8} }$

$\mathrm{Q11.\ If\ \bigg(\dfrac{p}{q}\bigg) = \bigg(\dfrac{3}{4}\bigg)^{18} \div \bigg(\dfrac{3}{4}\bigg)^{16}\ find\ \bigg(\dfrac{p}{q}\bigg)^2 }$

Solution :

Q10.

$\longmapsto \mathrm{6^x = 216}$

$\implies \mathrm{We\ know\ that,\ 6^3 = 216}$

$\implies \mathrm{6^x = 6^3}$

$\therefore \underline{\boxed{\mathbf{x=3}}}$

Now, we have to find the value of $\mathrm{5^{3x-8}}$

As x = 3, substituting it we get,

$\implies \mathrm{5^{3(3) - 8}}$

$\implies \mathrm{5^{9-8}}$

$\implies \mathrm{5^1}$

$\therefore \underline{\boxed{\mathbf{5^{3x-8}\bigg|_{x=3} = 5}}}$

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Q11.

$\longmapsto \mathrm{\bigg(\dfrac{p}{q}\bigg) = \bigg(\dfrac{3}{4}\bigg)^{18} \div \bigg(\dfrac{3}{4}\bigg)^{16}}$

We know that,

$\boxed{\mathrm{a^m \div a^n = a^{m-n} \ ; \ if\ m>n}}$

Here, m = 18 and n = 16 and thus, m > n; a = 3/4

$\implies \mathrm{\bigg(\dfrac{p}{q}\bigg) = \bigg(\dfrac{3}{4}\bigg)^{18} \div \bigg(\dfrac{3}{4}\bigg)^{16}}$

$\implies \mathrm{\bigg(\dfrac{p}{q}\bigg) = \bigg(\dfrac{3}{4}\bigg)^{18-16}}$

$\implies \mathrm{\bigg(\dfrac{p}{q}\bigg) = \bigg(\dfrac{3}{4}\bigg)^{2}}$

Now, squaring on both sides

$\implies \mathrm{\bigg(\dfrac{p}{q}\bigg)^2 = \Bigg(\bigg(\dfrac{3}{4}\bigg)^{2}\Bigg)^2}$

We know that,

$\boxed{\mathrm{(a^m)^n = a^{mn}}}$

Here, a = 3/4 ; m = 2, n = 2

So,

$\implies \mathrm{\bigg(\dfrac{p}{q}\bigg)^2 = \bigg(\dfrac{3}{4}\bigg)^{2 \times 2}}$

$\implies \mathrm{\bigg(\dfrac{p}{q}\bigg)^2 = \bigg(\dfrac{3}{4}\bigg)^{4}}$

$\therefore \underline{\boxed{\mathbf{\bigg(\dfrac{p}{q}\bigg)^2 = \bigg(\dfrac{81}{256}\bigg)}}}$

Hope it helps!!