What is 3ln(10)-log_{10}(5)-log_{10}(2) ?

The solution to 3ln(10)-log_{10}(5)-log_{10}(2) is 3ln(10)-1

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simplify 3ln(10)-log_{10}(5)-log_{10}(2)

simplify

3 ln (10) - lo g_{10} (5) - lo g_{10} (2)

3 ln (10) - 1

Decimal Notation

5.90775 \dots

Solution steps

3 ln (10) - lo g_{10} (5) - lo g_{10} (2)

Rewrite

- lo g_{10} (5) - lo g_{10} (2)

- (lo g_{10} (5) + lo g_{10} (2))

= 3 ln (10) - (lo g_{10} (5) + lo g_{10} (2))

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (5) + lo g_{10} (2) = lo g_{10} (5 \cdot 2)

= 3 ln (10) - lo g_{10} (5 \cdot 2)

Multiply the numbers:

5 \cdot 2 = 10

= 3 ln (10) - lo g_{10} (10)

Apply log rule:

lo g_{a} (a) = 1

= 3 ln (10) - 1

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What is 3ln(10)-log_{10}(5)-log_{10}(2) ?
The solution to 3ln(10)-log_{10}(5)-log_{10}(2) is 3ln(10)-1