To convert a logarithmic equation to its exponential form, we need to understand the relationship between logarithms and exponents. The logarithmic equation given is [tex]\(\log_6 7776 = 5\)[/tex]. In logarithmic form, [tex]\(a \log_b c = d\)[/tex] means [tex]\(b^d = c\)[/tex], where:
- [tex]\(b\)[/tex] is the base of the logarithm
- [tex]\(d\)[/tex] is the exponent
- [tex]\(c\)[/tex] is the result
Given the equation [tex]\(\log_6 7776 = 5\)[/tex]:
1. Identify the base [tex]\(b\)[/tex]. In this case, [tex]\(b = 6\)[/tex].
2. Identify the exponent [tex]\(d\)[/tex]. Here, [tex]\(d = 5\)[/tex].
3. The result [tex]\(c\)[/tex] is given as 7776.
Using these values, we can rewrite the logarithmic equation in exponential form which states that the base raised to the exponent equals the result:
[tex]\[6^5 = 7776\][/tex]
So, the exponential form of the equation [tex]\(\log_6 7776 = 5\)[/tex] is:
[tex]\[6^5 = 7776\][/tex]
