Join the IDNLearn.com community and start exploring a world of knowledge today. Join our community to receive prompt and reliable responses to your questions from knowledgeable professionals.
Sagot :
Certainly! Let's solve the given equation step-by-step.
The equation is:
[tex]\[ \log_2 (2z + 1) = 2 + \log_2 2 \][/tex]
### Step 1: Simplify the right-hand side
First, we simplify the term on the right-hand side of the equation.
We know that:
[tex]\[ \log_2 2 = 1 \][/tex]
So the equation simplifies to:
[tex]\[ \log_2 (2z + 1) = 2 + 1 \][/tex]
[tex]\[ \log_2 (2z + 1) = 3 \][/tex]
### Step 2: Convert the logarithmic equation to an exponential equation
To remove the logarithm, we convert the logarithmic equation to its exponential form:
[tex]\[ 2z + 1 = 2^3 \][/tex]
### Step 3: Solve the exponential equation
Next, we simplify the right-hand side:
[tex]\[ 2z + 1 = 8 \][/tex]
Subtract 1 from both sides:
[tex]\[ 2z = 7 \][/tex]
Divide both sides by 2:
[tex]\[ z = \frac{7}{2} \][/tex]
### Conclusion
The solution to the equation [tex]\(\log_2 (2z + 1) = 2 + \log_2 2\)[/tex] is:
[tex]\[ z = \frac{7}{2} \][/tex]
So, the value of [tex]\(z\)[/tex] is:
[tex]\[ z = 3.5 \][/tex]
The equation is:
[tex]\[ \log_2 (2z + 1) = 2 + \log_2 2 \][/tex]
### Step 1: Simplify the right-hand side
First, we simplify the term on the right-hand side of the equation.
We know that:
[tex]\[ \log_2 2 = 1 \][/tex]
So the equation simplifies to:
[tex]\[ \log_2 (2z + 1) = 2 + 1 \][/tex]
[tex]\[ \log_2 (2z + 1) = 3 \][/tex]
### Step 2: Convert the logarithmic equation to an exponential equation
To remove the logarithm, we convert the logarithmic equation to its exponential form:
[tex]\[ 2z + 1 = 2^3 \][/tex]
### Step 3: Solve the exponential equation
Next, we simplify the right-hand side:
[tex]\[ 2z + 1 = 8 \][/tex]
Subtract 1 from both sides:
[tex]\[ 2z = 7 \][/tex]
Divide both sides by 2:
[tex]\[ z = \frac{7}{2} \][/tex]
### Conclusion
The solution to the equation [tex]\(\log_2 (2z + 1) = 2 + \log_2 2\)[/tex] is:
[tex]\[ z = \frac{7}{2} \][/tex]
So, the value of [tex]\(z\)[/tex] is:
[tex]\[ z = 3.5 \][/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com is committed to providing the best answers. Thank you for visiting, and see you next time for more solutions.