High School

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Fill in each box below with an integer or a reduced fraction.

(a) [tex]\log _2 4=2[/tex] can be written in the form [tex]2^A=B[/tex] where [tex]A=[/tex] [tex]\square[/tex] and [tex]B=[/tex] [tex]\square[/tex]

(b) [tex]\log _5 3125=5[/tex] can be written in the form [tex]5^C=D[/tex] where [tex]C=[/tex] [tex]\square[/tex] and [tex]D=[/tex] [tex]\square[/tex]

Answer :

Recall that the logarithm $\log_b a = c$ means that the base $b$ raised to the power $c$ equals $a$, i.e.,
$$
b^c = a.
$$

Let's apply this definition to the two parts:

1. For part (a): We are given
$$
\log_2 4 = 2.
$$
This means that
$$
2^2 = 4.
$$
Thus, the expression can be written in the form
$$
2^A = B,
$$
where $A = 2$ and $B = 4$.

2. For part (b): We are given
$$
\log_5 3125 = 5.
$$
This means that
$$
5^5 = 3125.
$$
Thus, the expression can be written in the form
$$
5^C = D,
$$
where $C = 5$ and $D = 3125$.

In summary:

- For part (a): $A = 2$ and $B = 4$.
- For part (b): $C = 5$ and $D = 3125$.

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