Answer:
The log equation is given such as
![\log _(5x)\left(x\right)=(7)/(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/yzywtf6twnlkl22avl7brfsbx7gcmwguca.png)
The log equation as an exponential equation is:
![\:5x^{(7)/(2)}=x](https://img.qammunity.org/2022/formulas/mathematics/high-school/8c8rllv8724td6uag41vkalpqeqymhmqxf.png)
Explanation:
Given
The log equation is given such as
![\log _(5x)\left(x\right)=(7)/(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/yzywtf6twnlkl22avl7brfsbx7gcmwguca.png)
To determine
Write the log equation as an exponential equation.
Given the log equation
![\log _(5x)\left(x\right)=(7)/(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/yzywtf6twnlkl22avl7brfsbx7gcmwguca.png)
Apply the logarithmic definition.
![\log _ab=n\:\:\:\:\Rightarrow \:\:\:a^n=b](https://img.qammunity.org/2022/formulas/mathematics/high-school/hqa497z9k43pdk5yxmtzyzwcz0n5gx3ygx.png)
Thus,
![\:5x^{(7)/(2)}=x](https://img.qammunity.org/2022/formulas/mathematics/high-school/8c8rllv8724td6uag41vkalpqeqymhmqxf.png)