Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
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 visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.