Respuesta :

Answer:

The value of given expression  [tex]log_7343[/tex] is 3.

Step-by-step explanation:

 Given: [tex]log_7343[/tex]

We have to find the value of given expression  [tex]log_7343[/tex]

Consider  the given expression  [tex]log_7343[/tex]

Rewrite 343 in  base- power form as [tex]343=7^3[/tex]

We have

[tex]=\log _7\left(7^3\right)[/tex]

Apply log rule, [tex]\log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]

We have ,

[tex]\log _7\left(7^3\right)=3\log _7\left(7\right)[/tex]

Again Apply log rule [tex]\log _a\left(a\right)=1[/tex]

we have [tex]\log _7\left(7\right)=1[/tex]

Thus, [tex]3\log _7\left(7\right)=3[/tex]

Thus, the value of given expression  [tex]log_7343[/tex] is 3.

facundo3141592

By rewriting the given expression with natural logarithms, we will see that:

log₇(343) = 2.99

How to find logarithms that aren't the natural logarithm?

There is a really simple rule for logarithms of base different than e, that can be written as:

logₐ(x) = ln(x)/ln(a)

Then the given equation:

log₇(343) can be rewritten as:

log₇(343) = ln(343)/ln(7)

Now we have only natural logarithms, and we can evaluate that using a calculator:

ln(343)/ln(7) = 5.84/1.95 = 2.99

If you want to learn more about natural logarithms, you can read:

https://brainly.com/question/2499600

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