Respuesta :

kudzordzifrancis

Answer:

[tex]\log_{7}(2401) = 4[/tex]

Step-by-step explanation:

The given exponential equation is ;

[tex] {7}^{4} = 2401[/tex]

In this equation the power is on the left, with the base being 7 and the exponent being 4.

In the corresponding logarithmic equation:

7 becomes the base, 2401 becomes the number , and 4 becomes the results.

The corresponding logarithmic form is

[tex] \log_{7}(2401) = 4[/tex]

danielmaduroh

Explanation:

Here we have the following equation:

[tex]7^4=2401[/tex]

Applying log to both sides we get:

[tex]log(7^4)=log(2401) \\ \\ \\ But: \\ \\ 2401=4\times 343 \\ \\ \\ So: \\ \\ log(7^4)=log(7\times 343) \\ \\ \\ Properties: \\ \\ log(x^n)=nlog(x) \\ \\ log(xy)=log(x)+log(y) \\ \\ \\ Therefore: \\ \\ 4log(7)=log(7)+log(343) \\ \\ 4log(7)-log(7)=log(343) \\ \\ \boxed{3log(7)=log(343)}[/tex]

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