What is log_{10}(4)(64) ?

The solution to log_{10}(4)(64) is 128log_{10}(2)

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simplify log_{10}(4)(64)

simplify

lo g_{10} (4) (64)

128 lo g_{10} (2)

Decimal Notation

38.53183 \dots

Solution steps

lo g_{10} (4) (64)

Apply rule:

(a) = a

(64) = 64

= lo g_{10} (4) \cdot 64

Factor the number:

4 = 2^{2}

= lo g_{10} (2^{2}) \cdot 64

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 64

Multiply the numbers:

2 \cdot 64 = 128

= 128 lo g_{10} (2)

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