Solve the logarithmic equation by x log_2(x^2+7)+log_3(x+6)=6

Alessandra Cummings

Alessandra Cummings

Answered question

2022-11-01

Solve the logarithmic equation by x
log 2 ( x 2 + 7 ) + log 3 ( x + 6 ) = 6
What I tried: log 2 ( x 2 + 7 ) = a and log 3 ( x + 6 ) = b, then a + b = 6 and 2 a = 3 2 b 4 3 b + 1 + 43. But the problem is a and b don't have to be integers...>br?It is easy to show that for x > 3 and 3 > x 0 there are no soultions. Which leaves us only with the interval 0 > x > 6

Answer & Explanation

latatuy

latatuy

Beginner2022-11-02Added 12 answers

Take derivative and consider where left part increases and decreases, where are extrema (at least approximately). After proving that it has a single root, we can guess that it is x = 3
Madilyn Quinn

Madilyn Quinn

Beginner2022-11-03Added 2 answers

Hint: x is a natural number. Also l o g 2 ( x 2 + 7 ) and l o g 3 ( x + 6 ) are natural numbers. You will end up with 4 + 2 = 6

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?