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Which equation is equivalent to [tex]\log _3(x+5)=2[/tex]?

A. [tex]3^2=\left[\log _3(x+5)\right]^3[/tex]
B. [tex]2^3=\left[\log _3(x+5)\right]^2[/tex]
C. [tex]3^2=x+5[/tex]
D. [tex]2^3=x+5[/tex]

Sagot :

GinnyAnsweridn
To determine which equation is equivalent to [tex]\(\log_3(x + 5) = 2\)[/tex], let's rewrite this logarithmic equation in its exponential form.

The logarithmic equation [tex]\(\log_b(a) = c\)[/tex] can be rewritten as [tex]\(a = b^c\)[/tex].

So, starting with:
[tex]\[ \log_3(x + 5) = 2 \][/tex]

We can rewrite this as:
[tex]\[ x + 5 = 3^2 \][/tex]

Now, we need to compute [tex]\(3^2\)[/tex]:
[tex]\[ 3^2 = 9 \][/tex]

Thus, the equation simplifies to:
[tex]\[ x + 5 = 9 \][/tex]

Among the provided choices, the equation [tex]\(x + 5 = 9\)[/tex] is equivalent to the third option:
[tex]\[ 3^2 = x + 5 \][/tex]

So, the correct choice is:
3. [tex]\(3^2 = x + 5\)[/tex]
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