Solve the equation. \log_{6}(x+5)+\log_{6}x=2

sanuluy

sanuluy

Answered question

2021-10-02

Solve the equation.
log6(x+5)+log6x=2

Answer & Explanation

Alannej

Alannej

Skilled2021-10-03Added 104 answers

Step 1
We have to solve the equation:
log6(x+5)+log6x=2
We know the logarithmic property,
loga(b)+loga(c)=loga(bc)
loga(b)=cb=ac
Applying above property for the given equation, we get
log6(x+5)+log6(x)=2
log6(x+5)(x)=2
log6(x2+5x)=2
(x2+5x)=62
x2+5x=36
x2+5x36=0
Now solving the equation by middle term splitting method, we get
x2+5x36=0
x2+9x4x36=0
x(x+9)4(x+9)=0
(x+9)(x4)=0
Step 2
Either,
x+9=0
x=9
or,
x4=0
x=4
We know that for any logarithmic function log(f(x)),
f(x)>0
But here at x=9,log(x) is not defined therefore x=9 is not the solution.
Hence, solution of the equation is x=4.

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?