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Given that: log10 (7a + 2) = log10 (a – 4) + 1,  what is the integer value of ‘a’?

Given that: log10 (7a + 2) = log10 (a – 4) + 1,  what is the integer value of ‘a’? Correct Answer 14

GIVEN:

log10(7a + 2) = log10(a – 4) + 1

CONCEPT:

1 = log1010

FORMULA USED:

Property:

loga(P × Q) = logaP + logaQ

CALCULATION:

log10(7a + 2) = log10(a – 4) + 1

⇒ log10(7a + 2) = log10(a – 4) + log1010

⇒ log10(7a + 2) = log10

After comparing:

7a + 2 = 10(a – 4)

⇒ 3a = 42

⇒ a = 14

∴ Integer value of a = 14

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