The question is from logs
Find 'x' satisfying equation $4^{\log_{10} {x+1}} – 6^{\log_{10} x} – 2.3^{\log_{10} {x^2 +2}}$ = 0
I've tried to solve it. I was trying to convert base 10 of logs to respective numbers. like 4 for first one 6 for second one and 2.3 for third one. I thought that I'll be able to move those logs from powers. But I'm not able to figure how I convert them .
Please explain I can solve it. And Please solve it like a class 11th student.
Best Answer
The above expression is reducible to:
$$4\times 2^{2\log(x)} - 6^{\log(x)} - 18 \times 3^{2 \log(x)} = 0$$
Now let $ 2^{\log(x)} = a$ and $3^{\log(x)} = b$.
The above expression then becomes:
$$4a^2-ab-18b^2 = 0$$
Now factorize and solve for $x$!