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]
