Answered

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If [tex]$2^x=16$[/tex], then [tex]$3^x=$[/tex]

A. 12
B. 24
C. 48
D. 81

Sagot :

GinnyAnswer
To solve the given problem, we start by analyzing the equation [tex]\(2^x = 16\)[/tex].

Step 1: Express 16 as a power of 2.
We know that:
[tex]\[ 16 = 2^4 \][/tex]
So, we can write:
[tex]\[ 2^x = 2^4 \][/tex]

Step 2: Since the bases are the same on both sides of the equation, we can equate the exponents:
[tex]\[ x = 4 \][/tex]

Step 3: Now, we need to find the value of [tex]\(3^x\)[/tex] using the value of [tex]\(x\)[/tex] we just found:
[tex]\[ x = 4 \][/tex]
Thus:
[tex]\[ 3^x = 3^4 \][/tex]

Step 4: Calculate [tex]\(3^4\)[/tex]:
[tex]\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \][/tex]

Therefore, [tex]\(3^x = 81\)[/tex], and the correct answer is:
[tex]\[ \boxed{81} \][/tex]

So the answer is:
D 81
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