Question

Solve for x: log3(X)+ log3(X-2) = log3 (X+10)

Answer 1

Step-by-step explanation:

Given :-

log3(X)+ log3(X-2) = log3 (X+10)

To find:-

Solve for x: log3(X)+ log3(X-2) = log3 (X+10)

Solution:-

Given equation is log3(X)+ log3(X-2) = log3 (X+10)

we know that

logx (a)+ log x(b) = logx (ab)

=>log3(X)(X-2) = log3(X+10)

Therefore, X(X-2) = X+10

=>X^2-2X = X+10

=>X^2 -2X -X -10 = 0

=>X^2 - 3X - 10 = 0

=>X^2 + 2X -5X -10 = 0

=>X(X+2) -5(X+2) = 0

=>(X + 2) (X - 5) = 0

=>X+2 = 0 (or) X-5 = 0

=> X = -2 and 5

Answer:-

The values of X for the given problem are

-2 and 5

Check:-

If X = 5 then

LHS:-

log3(X)+ log3(X-2)

=>log3(5) +log3 (5-2)

=>log3 (5)+log3 (3)

=>log3 (5×3)

=> log3 (15)

RHS:-

log3 (X+10)

=>log3(5+10)

=>log3(15)

LHS = RHS is true for X = 5

If X = -2 then

LHS:-

log3(X)+ log3(X-2)

=>log3(-2)+log3(-2-2)

=>log3(-2)+log3(-4)

=>log3(-2×-4)

=>log3 (8)

RHS:-

log3(X+10)

=]log3(-2+10)

=>log3(8)

LHS = RHS is true for X= -2

Used formula:-

• logX(a)+logX(b)=logX(ab)