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Popular >

simplify log_{10}(4)(16)

Solution

simplify

lo g_{10} (4) (16)

Solution

32 lo g_{10} (2)

+1

Decimal

9.63295 \dots

Solution steps

lo g_{10} (4) (16)

Apply rule:

(a) = a

(16) = 16

= lo g_{10} (4) \cdot 16

Factor the number:

4 = 2^{2}

= lo g_{10} (2^{2}) \cdot 16

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{10} (2^{2}) = 2 lo g_{10} (2)

= 2 lo g_{10} (2) \cdot 16

Multiply the numbers:

2 \cdot 16 = 32

= 32 lo g_{10} (2)

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Frequently Asked Questions (FAQ)

What is log_{10}(4)(16) ?
The solution to log_{10}(4)(16) is 32log_{10}(2)