Solve this from the exponent chapter but no irrelevant answers
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Question :- 7^(1-2x) * 49³ * 343 = 1/7^(-4)
Solution :-
→ 7^(1-2x) * 49³ * 343 = 1/7^(-4)
→ 7^(1 - 2x) * (7²)³ * (7)³ = 1/7^(-4)
→ 7^(1 - 2x) * (7)⁶ * (7)³ = 1/7^(-4)
using a^m * a^n * a^p = a^(m + n + p) in LHS,
→ 7^(1 - 2x + 6 + 3) = 1/7^(-4)
using a^(-m) = 1/a^m in RHS,
→ 7^(1 - 2x + 6 + 3) = 1/{1/7⁴}
→ 7^(1 - 2x + 6 + 3) = 7⁴
finally , using a^m = a^n , then, m = n , we get,
→ (1 - 2x + 6 + 3) = 4
→ (10 - 2x) = 4
→ 2x = 10 - 4
→ 2x = 6
→ x = 3 .
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