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Which are true of [tex]\( x = \log_{10} 478,255 \)[/tex]? Select all that apply.

A. [tex]\( x \ \textless \ 6 \)[/tex]
B. [tex]\( x = 6 \)[/tex]
C. [tex]\( x \ \textgreater \ 5 \)[/tex]
D. [tex]\( x \ \textless \ 5 \)[/tex]
E. [tex]\( x = 7 \)[/tex]



Answer :

GinnyAnswer
To address the problem at hand, we need to determine which statements about [tex]\( x = \log_{10} 478,255 \)[/tex] are true. Based on the given information, the value of [tex]\( x \)[/tex] is:

[tex]\[ x = 5.679659519130193 \][/tex]

We will now verify each of the statements:

#### Statement a: [tex]\( x < 6 \)[/tex]
To verify:
[tex]\[ 5.679659519130193 < 6 \][/tex]
This statement is true.

#### Statement b: [tex]\( x = 6 \)[/tex]
To verify:
[tex]\[ 5.679659519130193 = 6 \][/tex]
This statement is false because [tex]\( x \)[/tex] is not equal to 6.

#### Statement c: [tex]\( x > 5 \)[/tex]
To verify:
[tex]\[ 5.679659519130193 > 5 \][/tex]
This statement is true.

#### Statement d: [tex]\( x < 5 \)[/tex]
To verify:
[tex]\[ 5.679659519130193 < 5 \][/tex]
This statement is false because [tex]\( x \)[/tex] is greater than 5.

#### Statement e: [tex]\( x = 7 \)[/tex]
To verify:
[tex]\[ 5.679659519130193 = 7 \][/tex]
This statement is false because [tex]\( x \)[/tex] is not equal to 7.

In summary, the true statements about [tex]\( x = \log_{10} 478,255 \)[/tex] are:

- [tex]\( x < 6 \)[/tex]
- [tex]\( x > 5 \)[/tex]

So, the true statements are:
- a. [tex]\( x < 6 \)[/tex]
- c. [tex]\( x > 5 \)[/tex]

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