Find the value of x, if 34 × 3x = 38.
4
When powers of the same base are multiplied, the exponents are added: \(a^m \times a^n = a^{m+n}\). If two powers of the same base (other than 0, 1 or −1) are equal, their exponents must be equal.
Step 1 — Combine the left side: \(3^4 \times 3^x = 3^{4+x}\).
Step 2 — Equate exponents: \(3^{4+x} = 3^8 \Rightarrow 4 + x = 8 \Rightarrow x = 4\).
Check: \(3^4 \times 3^4 = 81 \times 81 = 6561 = 3^8\). The value 12 comes from adding instead of subtracting 4, 2 from dividing 8 by 4, and 32 from multiplying; none of these satisfies the equation, and the remaining choice does not apply.
4 option is correct.
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