Answer :
To translate the logarithmic statement [tex]\(\log_5 3125 = 5\)[/tex] into an equivalent exponential statement, we need to understand what each part of the logarithmic statement means.
In logarithmic form, [tex]\(\log_b a = c\)[/tex], [tex]\(b\)[/tex] is the base, [tex]\(a\)[/tex] is the number, and [tex]\(c\)[/tex] is the exponent. This means that [tex]\(b\)[/tex] raised to the power of [tex]\(c\)[/tex] results in [tex]\(a\)[/tex].
Given the logarithmic statement [tex]\(\log_5 3125 = 5\)[/tex], we can identify the parts as follows:
- The base [tex]\(b\)[/tex] is 5.
- The result or number [tex]\(a\)[/tex] is 3125.
- The exponent [tex]\(c\)[/tex] is 5.
To convert this into an exponential statement, we use the rule: [tex]\(b^c = a\)[/tex].
So, in this case:
[tex]\[5^5 = 3125\][/tex]
Therefore, the equivalent exponential equation is [tex]\(5^5 = 3125\)[/tex].
In logarithmic form, [tex]\(\log_b a = c\)[/tex], [tex]\(b\)[/tex] is the base, [tex]\(a\)[/tex] is the number, and [tex]\(c\)[/tex] is the exponent. This means that [tex]\(b\)[/tex] raised to the power of [tex]\(c\)[/tex] results in [tex]\(a\)[/tex].
Given the logarithmic statement [tex]\(\log_5 3125 = 5\)[/tex], we can identify the parts as follows:
- The base [tex]\(b\)[/tex] is 5.
- The result or number [tex]\(a\)[/tex] is 3125.
- The exponent [tex]\(c\)[/tex] is 5.
To convert this into an exponential statement, we use the rule: [tex]\(b^c = a\)[/tex].
So, in this case:
[tex]\[5^5 = 3125\][/tex]
Therefore, the equivalent exponential equation is [tex]\(5^5 = 3125\)[/tex].
