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Popular >

simplify 243^{log_{27}(125)}

Solution

simplify

24 3^{l o g_{27} (125)}

Solution

3125

Solution steps

24 3^{l o g_{27} (125)}

lo g_{27} (125) = lo g_{3} (5)

= 24 3^{l o g_{3} (5)}

Factor the number:

243 = 3^{5}

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

Apply exponent rule:

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

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

Apply exponent rule:

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

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

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

Apply log rule:

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

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

= 5^{5}

5^{5} = 3125

= 3125

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Frequently Asked Questions (FAQ)

What is 243^{log_{27}(125)} ?
The solution to 243^{log_{27}(125)} is 3125