Question

Tercise 5.2What is the value of n if275Ctimes%209%20%7D%5E4" id="TexFormula1" title="3 {?}^{5 \times } \times 9 }^4" alt="3 {?}^{5 \times } \times 9 }^4" align="absmiddle" class="latex-formula">
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Answer 1

Explanation:

(32)n × 33 × 3n – (33)n/ (315 × 23) = (1/27) = 3(2n+2+n) – (33)n/ (315 × 23) = (1/27) = 3(3n+2)– (33)n/ (315 × 23) = (1/27) = 33n × 32 – 33n/ (315 × 23) = (1/27) = 33n × (32 – 1)/ (315 × 23) = (1/27) = 33n × (9 – 1)/ (315 × 23) = (1/27) = 33n × (8)/ (315 × 23) = (1/27) = 33n × 23/ (315 × 23) = (1/27) = 33n/315 = (1/27) = 33n-15 = (1/27) = 33n-15 = (1/33) = 33n-15 = 3-3

On equating the coefficients, we get

3n -15 = -3 ⇒

3n = -3 + 15

⇒ 3n = 12

⇒ n = 12/3 = 4