What is expand log_{5}((5^i)^2) ?

The solution to expand log_{5}((5^i)^2) is 2i

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expand log_{5}((5^i)^2)

expand

lo g_{5} ((5^{i})^{2})

2 i

Solution steps

lo g_{5} ((5^{i})^{2})

Apply log rule:

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

lo g_{5} ((5^{i})^{2}) = 2 lo g_{5} (5^{i})

= 2 lo g_{5} (5^{i})

Apply log rule:

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

lo g_{5} (5^{i}) = i lo g_{5} (5)

= 2 i lo g_{5} (5)

Simplify

lo g_{5} (5) : 1

= 2 \cdot 1 i

Multiply the numbers:

2 \cdot 1 = 2

= 2 i

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