Respuesta :

alinakincsem

Answer:

1

Step-by-step explanation:

We are to find the value of the following:

[tex] log _ 3 5 \times log _ { 2 5 } 9 [/tex]

[tex] \log _ { 3 } 5 \times \log _ { 2 5 } 9 =\dfrac{1}{\log_{5}3}\times\log_{25}9=\dfrac{1}{\log_{5}3}\times\log_{5^2}9=\dfrac{1}{\log_{5}3}\times\dfrac{1}{2}\log_{5}9[/tex]

[tex] \dfrac { 1 } { \log _ { 5 } 3 } \times \dfrac { 1 } { 2 } \log_ { 5 } 9 = \dfrac{1}{\log_{5}3}\cdot\dfrac{1}{2}\log_{5}3^2=\dfrac{1}{\log_{5}3}\cdot\dfrac{2}{2}\log_{5}3=\dfrac{1}{\log_{5}3}\cdot\log_{5}3=\dfrac{\log_{5}3}{\log_{5}3}=[/tex] 1

luisejr77

Answer:

The value is: 1

Step-by-step explanation:

Use the Change of base formula. This is:

[tex]log_a(x)=\frac{log_b(x)}{log_b(a)}[/tex]

Using base 10:

[tex]log_3(5)*log_{25}(9)=\frac{log(5)}{log(3)}*\frac{log(9)}{log(25)}[/tex]

We know that:

[tex]9=3^2\\25=5^2[/tex]

And according to the logarithms properties:

[tex]log(x)^n=nlog(x)[/tex]

Then, we can simplify the expression:

[tex]=\frac{log(5)}{log(3)}*\frac{log(3)^2}{log(5)^2}=\frac{log(5)}{log(3)}*\frac{2log(3)}{2log(5)}=\frac{log(5)}{log(3)}*\frac{log(3)}{log(5)}=\frac{log(5)*log(3)}{log(3)*log(5)}=1[/tex]