Answer :
Sure! Let's express the logarithmic equations in exponential form.
### (a) The equation is [tex]\(\log_2 4 = 2\)[/tex].
To convert a logarithmic equation to its exponential form, we use the relationship:
[tex]\[
\log_{\text{base}}(\text{value}) = \text{result} \quad \implies \quad \text{base}^{\text{result}} = \text{value}
\][/tex]
For [tex]\(\log_2 4 = 2\)[/tex]:
- The base is 2,
- The result is 2,
- The value is 4.
So, the equation in exponential form is:
[tex]\[
2^2 = 4
\][/tex]
Thus, [tex]\(A = 2\)[/tex] and [tex]\(B = 4\)[/tex].
### (b) The equation is [tex]\(\log_5 3125 = 5\)[/tex].
Similarly, we apply the same relationship:
For [tex]\(\log_5 3125 = 5\)[/tex]:
- The base is 5,
- The result is 5,
- The value is 3125.
The exponential form is:
[tex]\[
5^5 = 3125
\][/tex]
Therefore, [tex]\(C = 5\)[/tex] and [tex]\(D = 3125\)[/tex].
So to summarize:
- For part (a): [tex]\(2^2 = 4\)[/tex] with [tex]\(A = 2\)[/tex] and [tex]\(B = 4\)[/tex].
- For part (b): [tex]\(5^5 = 3125\)[/tex] with [tex]\(C = 5\)[/tex] and [tex]\(D = 3125\)[/tex].
### (a) The equation is [tex]\(\log_2 4 = 2\)[/tex].
To convert a logarithmic equation to its exponential form, we use the relationship:
[tex]\[
\log_{\text{base}}(\text{value}) = \text{result} \quad \implies \quad \text{base}^{\text{result}} = \text{value}
\][/tex]
For [tex]\(\log_2 4 = 2\)[/tex]:
- The base is 2,
- The result is 2,
- The value is 4.
So, the equation in exponential form is:
[tex]\[
2^2 = 4
\][/tex]
Thus, [tex]\(A = 2\)[/tex] and [tex]\(B = 4\)[/tex].
### (b) The equation is [tex]\(\log_5 3125 = 5\)[/tex].
Similarly, we apply the same relationship:
For [tex]\(\log_5 3125 = 5\)[/tex]:
- The base is 5,
- The result is 5,
- The value is 3125.
The exponential form is:
[tex]\[
5^5 = 3125
\][/tex]
Therefore, [tex]\(C = 5\)[/tex] and [tex]\(D = 3125\)[/tex].
So to summarize:
- For part (a): [tex]\(2^2 = 4\)[/tex] with [tex]\(A = 2\)[/tex] and [tex]\(B = 4\)[/tex].
- For part (b): [tex]\(5^5 = 3125\)[/tex] with [tex]\(C = 5\)[/tex] and [tex]\(D = 3125\)[/tex].
