Question

(5^log(25) 9 + 3^log(9) 25)^log(2)5

Answer 1

$(5 ^{log _{25}9 } +3 ^{log _{9}25 } ) ^{log _{2}5 }=(5 ^{log _{5}3 }+ 3^{log _{3} 5}) ^{log _{2}5 }=(3+5) ^{log _{2} 5}=8 ^{log _{8}125 } =$ $=125$

Answer 2

Решение:
1)  $5^{ log_{25} 9} = 5^{ log_{ 5^{2} } 9} = 5^{ log_{ 5^{2} } 3^{2} } = 5^{ log_{5} 3} = 3$
2)  $3^{ log_{ 3^{2} } 5^{2} } = 3^{ log_{ 3 } 5 } = 5$
3)  $3 + 5 = 8$
4)  $8^{ log_{ 2 } 5} = (2^{ log_{ 2 } 5} )^{3} = 5^{3} = 125$
Ответ: 125.

Answer 3

To simplify the expression (5^log(25) 9 + 3^log(9) 25)^log(2)5, let's break it down step by step:

Step 1: Evaluate the exponents inside the logarithms. log(25) 9 = log base 25 of 9 = 1/2 log(9) 25 = log base 9 of 25 = 2/3

Step 2: Substitute the evaluated exponents into the expression. (5^(1/2) + 3^(2/3))^log(2)5

Step 3: Evaluate the base raised to the fractional exponents. 5^(1/2) = √5 3^(2/3) = ∛(3^2) = ∛9

Step 4: Substitute the evaluated base into the expression. (√5 + ∛9)^log(2)5

Step 5: Evaluate the logarithm base and simplify further. log(2)5 = log base 2 of 5 ≈ 2.32192

Step 6: Substitute the evaluated logarithm base into the expression. (√5 + ∛9)^2.32192

At this point, we can either leave the expression as it is or use a calculator to approximate the value.