Question

Write as
logarithm with base 4:
4
-5
2
-4

Answer 1

Answer:

log_4(256)=4

log_4(1/1024)=-5

log_4(16)=2

log_4(1/256)=-4

Step-by-step explanation:

We want to write a number, x, such that

Log_4(y)=x.

In exponential form that is 4^x=y.

So first number is x=4.

4^4=256 which means log_4(256) is 4 as a logarithm with base 4.

The second number is x=-5.

4^-5=1/4^5=1/1024 which means log_4(1/1024) is -5 as a logarithm with base 4.

The third number is x=2.

4^2=16 so log_4(16) is 2 as a logarithm with base 4.

The fourth number is x=-4.

Since 4^4=256 then 4^-4=1/256 which means -4 as a logarithm with base 4 is log_4(1/256).

Answer 2

The logarithmic expressions are: $\log_4(256) = 4$, $\log_4({4^{-5}}) = -5$, $\log_4({16) = 2$ and $\log_4({4^{-4}) = -4$

A number x written in logarithm form is represented as:

$\log_b(y)=x.$

Where:

$b^x=y$

Given that the base is 4, the equations become:

$\log_4(y) = x$

$4^x = y$

For number 4, we have:

$y = 4^4$

$y = 256$

This gives

$\log_4(256) = 4$

For number -5, we have:

$y = 4^{-5}$

This gives

$\log_4({4^{-5}}) = -5$

For number 2, we have:

$y = 4^{2}$

$y =16$

This gives

$\log_4({16) = 2$

For number -4, we have:

$y = 4^{-4}$

This gives

$\log_4({4^{-4}) = -4$

Hence, the logarithmic expressions are: $\log_4(256) = 4$, $\log_4({4^{-5}}) = -5$, $\log_4({16) = 2$ and $\log_4({4^{-4}) = -4$

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