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Popular >

simplify 27^{log_{3}(5)}

Solution

simplify

2 7^{l o g_{3} (5)}

Solution

125

Solution steps

2 7^{l o g_{3} (5)}

Factor the number:

27 = 3^{3}

= (3^{3})^{l o g_{3} (5)}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 3^{3 l o g_{3} (5)}

Apply exponent rule:

a^{b c} = (a^{b})^{c}, a \geq 0

3^{3 l o g_{3} (5)} = (3^{l o g_{3} (5)})^{3}

= (3^{l o g_{3} (5)})^{3}

Apply log rule:

a^{l o g_{a} (b)} = b

3^{l o g_{3} (5)} = 5

= 5^{3}

5^{3} = 125

= 125

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Frequently Asked Questions (FAQ)

What is 27^{log_{3}(5)} ?
The solution to 27^{log_{3}(5)} is 125