It is given that $$\log_a x^2+\log_a x^3=\log_a x+(\log_a x)^2$$ with $a$ and $x$ positive real

Question

It is given that $$\log_a x^2+\log_a x^3=\log_a x+(\log_a x)^2$$ with $a$ and $x$ positive real numbers and with $a\ne1$ and $x>1$. Find an expression of $x$ in terms of $a$.

Accepted Answer

$x=a^4$, with the given conditions requiring $a>1$.

IB Math HL January 2016 P1 Q1

IB Math HL January 2016 P1 Q1

Solution:

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