Certainly! Let's start with the given logarithmic equation:
[tex]\[
\log_{4x}(x) = \frac{9}{5}
\][/tex]
We want to rewrite this logarithmic equation in its equivalent exponential form. Recall that if:
[tex]\[
\log_b(a) = c
\][/tex]
then the equivalent exponential form is:
[tex]\[
b^c = a
\][/tex]
In our case, the base [tex]\( b \)[/tex] is [tex]\( 4x \)[/tex], the exponent [tex]\( c \)[/tex] is [tex]\( \frac{9}{5} \)[/tex], and the result [tex]\( a \)[/tex] is [tex]\( x \)[/tex]. Applying this to our equation:
[tex]\[
\log_{4x}(x) = \frac{9}{5}
\][/tex]
we get:
[tex]\[
(4x)^{\frac{9}{5}} = x
\][/tex]
Thus, the equivalent exponential form of the given logarithmic equation is:
[tex]\[
(4x)^{\frac{9}{5}} = x
\][/tex]
