At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Let's solve the given equation step by step:
We have:
[tex]\[ 2^{x+3} + 2^x = 36 \][/tex]
First, let's rewrite [tex]\( 2^{x+3} \)[/tex] using properties of exponents:
[tex]\[ 2^{x+3} = 2^x \cdot 2^3 = 2^x \cdot 8 \][/tex]
Now, substitute this back into the original equation:
[tex]\[ 8 \cdot 2^x + 2^x = 36 \][/tex]
Notice that both terms on the left-hand side have a common factor of [tex]\( 2^x \)[/tex]. So, we can factor out [tex]\( 2^x \)[/tex]:
[tex]\[ 2^x (8 + 1) = 36 \][/tex]
Simplify inside the parentheses:
[tex]\[ 2^x \cdot 9 = 36 \][/tex]
Now, divide both sides by 9 to solve for [tex]\( 2^x \)[/tex]:
[tex]\[ 2^x = \frac{36}{9} \][/tex]
Simplify the right-hand side:
[tex]\[ 2^x = 4 \][/tex]
We know that [tex]\( 4 \)[/tex] can be expressed as a power of 2:
[tex]\[ 4 = 2^2 \][/tex]
So:
[tex]\[ 2^x = 2^2 \][/tex]
Since the bases are the same, we can equate the exponents:
[tex]\[ x = 2 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] is:
[tex]\[ \boxed{2} \][/tex]
Thus the correct answer is:
a. 2
We have:
[tex]\[ 2^{x+3} + 2^x = 36 \][/tex]
First, let's rewrite [tex]\( 2^{x+3} \)[/tex] using properties of exponents:
[tex]\[ 2^{x+3} = 2^x \cdot 2^3 = 2^x \cdot 8 \][/tex]
Now, substitute this back into the original equation:
[tex]\[ 8 \cdot 2^x + 2^x = 36 \][/tex]
Notice that both terms on the left-hand side have a common factor of [tex]\( 2^x \)[/tex]. So, we can factor out [tex]\( 2^x \)[/tex]:
[tex]\[ 2^x (8 + 1) = 36 \][/tex]
Simplify inside the parentheses:
[tex]\[ 2^x \cdot 9 = 36 \][/tex]
Now, divide both sides by 9 to solve for [tex]\( 2^x \)[/tex]:
[tex]\[ 2^x = \frac{36}{9} \][/tex]
Simplify the right-hand side:
[tex]\[ 2^x = 4 \][/tex]
We know that [tex]\( 4 \)[/tex] can be expressed as a power of 2:
[tex]\[ 4 = 2^2 \][/tex]
So:
[tex]\[ 2^x = 2^2 \][/tex]
Since the bases are the same, we can equate the exponents:
[tex]\[ x = 2 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] is:
[tex]\[ \boxed{2} \][/tex]
Thus the correct answer is:
a. 2
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.