Logs on both sides

Algebra Level 1

Find the range of positive value of $x$ such that $\log_3 (x+7) < \log_9(x^2+77)$ is fulfilled?

2 < x Cannot be determined from given information 0 < x < 2 0 < x

1 solution

Denton Young
Feb 18, 2016

$log_{3} (x + 7) = log_{9} (x+7)^2$

$(x + 7)^2 < x^2 + 77$
$x^2 + 14x + 49 < x^2 + 77$
$14x + 49 < 77$
$14x < 28$
$x < 2$

And it is given that $x > 0$ , so $0 < x < 2$

Moderator note:

Nice setup. The solution could use a few more words to explain what is happening. Alternatively, use the implication sign $\Rightarrow$ to indicate that the equations follow from each other.

This is the easiest way to solve this problem

anukool srivastava - 3 years, 8 months ago

Where is it given x>0?

Adolphout H - 11 months, 1 week ago

"Find the range of positive value of x..."

Denton Young - 11 months, 1 week ago

OK, thank you.

Adolphout H - 5 months, 1 week ago

Logs on both sides

1 solution

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