Solve the logarithmic equation. Round your answer to two decimal places. $$\log _ { 2 } x + \log _ { 2 } ( x + 1 ) - \log _ { 2 } 3 = 4$$
A) $x = 2.00$
B) $x = - 3.00 ; x = 2.00$
C) $x = 6.45$
D) $x = - 7.45 ; x = 6.45$
E)none of these

Question

Quizplus · Accepted Answer

Using logarithm rules, we can simplify the equation as follows:
$$\log_2\left(\frac{x(x+1)}{3}\right)=4$$
$$\frac{x(x+1)}{3}=2^4=16$$
$$x^2+x-48=0$$
Solving for x, we get $x=6.45$ or $x=-7.45$. However, since we cannot take the logarithm of a negative number, we discard the negative solution. Therefore, the only valid solution is $x=6.45$.

Solve the Logarithmic Equation log⁡2x+log⁡2(x+1)−log⁡23=4\log _ { 2 } x + \log _ { 2 } ( x + 1 ) - \log _ { 2 } 3 = 4log2​x+log2​(x+1)−log2​3=4

Solve the Logarithmic Equation $\log _ { 2 } x + \log _ { 2 } ( x + 1 ) - \log _ { 2 } 3 = 4$