Alright! Let's begin by carefully transforming the given logarithmic equation into its corresponding exponential form.
The given logarithmic equation is:
[tex]\[ \log_{4x}(5x - 9) = 2x - 1 \][/tex]
A logarithmic equation of the form [tex]\(\log_b(a) = c\)[/tex] can be converted into its exponential form as [tex]\(b^c = a\)[/tex].
Now, let's identify the parts of our logarithmic equation:
- The base [tex]\(b\)[/tex] is [tex]\(4x\)[/tex].
- The argument [tex]\(a\)[/tex] is [tex]\(5x - 9\)[/tex].
- The result [tex]\(c\)[/tex] is [tex]\(2x - 1\)[/tex].
Applying the conversion rule, we get:
[tex]\[ (4x)^{2x - 1} = 5x - 9 \][/tex]
Thus, the exponential form of the equation [tex]\(\log_{4x}(5x - 9) = 2x - 1\)[/tex] is:
[tex]\[ (4x)^{2x - 1} = 5x - 9 \][/tex]
This completes the conversion from the logarithmic form to the exponential form.
