Answer:
2.62
Step-by-step explanation:
[tex]log_{b} \frac{b^{2}x^{\frac{5}{2} }}{\sqrt{y}}[/tex]
First, write the square root as exponent.
[tex]log_{b} \frac{b^{2}x^{\frac{5}{2} }}{y^{\frac{1}{2}}}[/tex]
Move the denominator to the numerator and negate the exponent.
[tex]log_{b}(b^{2}x^{\frac{5}{2}}y^{-\frac{1}{2}})[/tex]
Use log product property.
[tex]log_{b}(b^{2}) + log_{b}(x^{\frac{5}{2}}) + log_{b}(y^{-\frac{1}{2}})[/tex]
Use log exponent property.
[tex]2 log_{b}(b) + {\frac{5}{2}}log_{b}(x) - {\frac{1}{2}}log_{b}(y)[/tex]
Substitute values.
[tex]2(1) + \frac{5}{2}(0.36) - \frac{1}{2}(0.56) \\2.62[/tex]
