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Sagot :
Sure, let's solve the equation given:
[tex]\[ \sqrt{2^{x+5}} = 16 \][/tex]
Here's the step-by-step solution:
1. Square both sides to eliminate the square root:
[tex]\[ (\sqrt{2^{x+5}})^2 = 16^2 \][/tex]
This simplifies to:
[tex]\[ 2^{x+5} = 256 \][/tex]
2. Rewrite 256 as a power of 2:
[tex]\[ 256 = 2^8 \][/tex]
So the equation becomes:
[tex]\[ 2^{x+5} = 2^8 \][/tex]
3. Since the bases are the same, we can set the exponents equal to each other:
[tex]\[ x + 5 = 8 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x + 5 = 8 \][/tex]
[tex]\[ x = 8 - 5 \][/tex]
[tex]\[ x = 3 \][/tex]
Therefore, the solution is:
[tex]\[ x = 3 \][/tex]
[tex]\[ \sqrt{2^{x+5}} = 16 \][/tex]
Here's the step-by-step solution:
1. Square both sides to eliminate the square root:
[tex]\[ (\sqrt{2^{x+5}})^2 = 16^2 \][/tex]
This simplifies to:
[tex]\[ 2^{x+5} = 256 \][/tex]
2. Rewrite 256 as a power of 2:
[tex]\[ 256 = 2^8 \][/tex]
So the equation becomes:
[tex]\[ 2^{x+5} = 2^8 \][/tex]
3. Since the bases are the same, we can set the exponents equal to each other:
[tex]\[ x + 5 = 8 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x + 5 = 8 \][/tex]
[tex]\[ x = 8 - 5 \][/tex]
[tex]\[ x = 3 \][/tex]
Therefore, the solution is:
[tex]\[ x = 3 \][/tex]
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