solve the exponential equation using like bases 7^(x^2 +4x)=1/343

solve the exponential equation using like bases 7^(x^2 +4x)=1/343
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343=7^3, so we can write: 7^(x^2+4x)=1/7^3=7^-3. Therefore, equating exponents, x^2+4x=-3 so x^2+4x+3=0.

This quadratic factorises: (x+1)(x+3)=0 and x=-1 or -3. Check the answer by substituting for x in the original equation: 7^(1-4)=7^-3=1/343; 7^(9-12)=7^-3=1/343.

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