Question is to solve the equation for value of $x$.
$$9^{1+\log x} - 3^{1+\log x} - 210 = 0; \quad \text{where base of log is }3$$
The answer given is $x=5$
I've tried to solve it. And got two values of $x= -14/3$ and $x=5$. What I've done wrong?
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Asaf Karagila
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Piyush Mishra
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Use $a^{\log_b(x)} = x^{\log_b(a)}$. – ViktorStein Apr 20 '19 at 19:57
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1The final step should be $(3k+14)(k-5)=0$ (multiplication since you are factoring) This is what then allows you to reach your conclusion. – John Doe Apr 20 '19 at 20:00
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You have solved correctly just made one error towards the end. Note that the domain of $\log(x)$ is $x > 0$ so $x=-14/3$ is rejected as it is not in the domain of the function.
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2Yep. And going from $(3 x + 14) + (x - 5) = 0$ does not mean that either term in the sum is $0$. – David G. Stork Apr 20 '19 at 19:58
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He meant$(3x+14)(x-5) = 0$. He was solving a quadratic. Must be $\times$ in the middle. – Vizag Apr 20 '19 at 20:00
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