Given:
[tex]log_2(2x+9)=2[/tex]
Required:
We need to solve the given equation.
Explanation:
Consider the formula.
[tex]log_a(b)=x\Rightarrow a^x=b.[/tex]
The given equation can be written as follows.
[tex]2^2=2x+9[/tex]
[tex]4=2x+9[/tex]
Solve for x.
[tex]4=2x+9[/tex]
Subtract 9 from both sides of the equation.
[tex]4-9=2x+9-9[/tex]
[tex]-5=2x[/tex]
Divide both sides by 2.
[tex]-\frac{5}{2}=\frac{2x}{2}[/tex][tex]-\frac{5}{2}=x[/tex]
Final answer:
Rewrite the given equation without logrithmic.
[tex]4=2x+9[/tex]
The solution for x.
[tex]x=-\frac{5}{2}[/tex]
