Respuesta :

gmany
[tex]\log_35\cdot\log_{25}9=\log_35\cdot\log_{25}3^2\\\\/use:\ \log x^n=n\log x/\\\\=\log_35\cdot2\log_{25}3\\\\/use:\log_ab=\dfrac{1}{\log_ba}/\\\\=\log_35\cdot2\cdot\dfrac{1}{\log_325}=\log_35\cdot\dfrac{2}{\log_35^2}=\dfrac{2\log_35}{2\log_35}=1[/tex]

The value of the logarithmic expression log₃ 5 x log₂₅ 9 will be 1.

What is a logarithm?

Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.

The expression is given below.

⇒ log₃ 5 x log₂₅ 9

We know that logₐb = log b / log a.

⇒ (log 5 / log 3) x (log 9 / log 25)

⇒ (log 5 / log 3) x (log 3² / log 5²)

We know that log a² = 2 log a.

⇒ (log 5 / log 3) x (2 log 3 / 2log 5)

⇒ 1

More about the logarithm link is given below.

https://brainly.com/question/7302008

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