Question

What are the solutions to log3x + log3(x2 + 2) = 1 + 2log3x?

Answer 1

Answer:

Option C and D are correct

x = 1

x= 2

Step-by-step explanation:

Use logarithmic rules:

$\log_b b = 1$

$\log_b (mn) = \log_b m+ \log_b n$

$\log_b x^n = n\log_b x$

As per the statement:

Given the equation:

$\log_3 x+ \log_3 (x^2+2) = 1+2\log_3 x$

Apply the logarithmic rules:'

$\log_3 x(x^2+2) = \log_3 3 + \log_3 x^2$

Again apply logarithmic rule:

$\log_3 x(x^2+2) =\log_3 3x^2$

then;

$x(x^2+2) = 3x^2$

Divide both sides by x we have;

$x^2+2 = 3x$

Subtract 3x from both sides we have;

$x^2-3x+2=0$

⇒$x^2-2x-x+2=0$

⇒$x(x-2)-1(x-2)=0$

⇒$(x-2)(x-1)=0$

By zero product property we have;

x-2 = 0 and x-1 = 0

⇒x = 2 and x = 1

Therefore, the solution for the given equation are: 1 and 2

Answer 2

X=1 & x=2 is the answer i dont know how to explain it but i got it right.