(b) Diberi bahawa $$ 9^{2 p q+1}+3^{4 p q-3}=732 $$, ungkapkan $$ p $$ dalam sebutan $$ q $$. Given that $$ 9^{2 p q+1}+3^{4 p q-3}=732 $$, express $$ p $$ in terns of $$ q $$.

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UpStudy AI · Accepted Answer

Given the equation:

$$
9^{2pq + 1} + 3^{4pq - 3} = 732
$$

Let's express everything in terms of base $$ 3 $$:

$$
9 = 3^2 \quad \text{so} \quad 9^{2pq + 1} = (3^2)^{2pq + 1} = 3^{4pq + 2}
$$

The equation becomes:

$$
3^{4pq + 2} + 3^{4pq - 3} = 732
$$

Let $$ x = 3^{4pq} $$. Then:

$$
3^{4pq + 2} = x \cdot 3^2 = 9x \
3^{4pq - 3} = \frac{x}{3^3} = \frac{x}{27}
$$

Substituting these into the equation:

$$
9x + \frac{x}{27} = 732
$$

Multiply both sides by $$ 27 $$ to eliminate the fraction:

$$
243x + x = 19764 \
244x = 19764 \
x = \frac{19764}{244} = 81 \quad (\text{since } 244 \times 81 = 19764)
$$

Recall that $$ x = 3^{4pq} $$, so:

$$
3^{4pq} = 81 = 3^4
$$

Equating the exponents:

$$
4pq = 4 \
pq = 1 \
p = \frac{1}{q}
$$

**Jawapan:** $$ p = \dfrac{1}{\,q\,} $$
$$ p = \dfrac{1}{q} $$

(b) Diberi bahawa \( 9^{2 p q+1}+3^{4 p q-3}=732 \), ungkapkan \( p \) dalam sebutan \( q \). Given that \( 9^{2 p q+1}+3^{4 p q-3}=732 \), express \( p \) in terns of \( q \).

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