Answer :
To convert the exponential equation [tex]\(9^2 = 81\)[/tex] into logarithmic form, you can follow these steps:
1. Identify the Parts of the Exponential Equation: The equation is [tex]\(a^b = c\)[/tex], where:
- [tex]\(a\)[/tex] is the base,
- [tex]\(b\)[/tex] is the exponent, and
- [tex]\(c\)[/tex] is the result.
In this case, [tex]\(a = 9\)[/tex], [tex]\(b = 2\)[/tex], and [tex]\(c = 81\)[/tex].
2. Understand the Logarithmic Form: The equivalent logarithmic form of the equation [tex]\(a^b = c\)[/tex] is [tex]\(\log_a(c) = b\)[/tex]. This means you are seeking the exponent [tex]\(b\)[/tex] to which the base [tex]\(a\)[/tex] must be raised to achieve the result [tex]\(c\)[/tex].
3. Apply to the Given Equation: With [tex]\(a = 9\)[/tex], [tex]\(b = 2\)[/tex], and [tex]\(c = 81\)[/tex], you substitute these into the logarithmic form:
[tex]\[
\log_9(81) = 2
\][/tex]
This expression means that the power to which 9 must be raised to produce 81 is 2.
Therefore, the correct logarithmic form of the equation [tex]\(9^2 = 81\)[/tex] is [tex]\(\log_9(81) = 2\)[/tex], which matches option D.
1. Identify the Parts of the Exponential Equation: The equation is [tex]\(a^b = c\)[/tex], where:
- [tex]\(a\)[/tex] is the base,
- [tex]\(b\)[/tex] is the exponent, and
- [tex]\(c\)[/tex] is the result.
In this case, [tex]\(a = 9\)[/tex], [tex]\(b = 2\)[/tex], and [tex]\(c = 81\)[/tex].
2. Understand the Logarithmic Form: The equivalent logarithmic form of the equation [tex]\(a^b = c\)[/tex] is [tex]\(\log_a(c) = b\)[/tex]. This means you are seeking the exponent [tex]\(b\)[/tex] to which the base [tex]\(a\)[/tex] must be raised to achieve the result [tex]\(c\)[/tex].
3. Apply to the Given Equation: With [tex]\(a = 9\)[/tex], [tex]\(b = 2\)[/tex], and [tex]\(c = 81\)[/tex], you substitute these into the logarithmic form:
[tex]\[
\log_9(81) = 2
\][/tex]
This expression means that the power to which 9 must be raised to produce 81 is 2.
Therefore, the correct logarithmic form of the equation [tex]\(9^2 = 81\)[/tex] is [tex]\(\log_9(81) = 2\)[/tex], which matches option D.
