Question

(25^log5 (корень из 3-1)+9^log3(корень из 3+1)*log3 5/log3 625

Answer 1

$(25^{log_5( \sqrt{3}-1 )}+9^{log_3( \sqrt{3}+1) })* \frac{log_3 5}{log_3 625} =$
$(5^{2log_5( \sqrt{3}-1 )}+3^{2log_3( \sqrt{3}+1) })*log_{625}5=$
$(( \sqrt{3} -1)^2+( \sqrt{3}+1)^2 )*log_{5^{4}}5=$
$(3-2 \sqrt{3}+1 +3+2 \sqrt{3}+1) * \frac{1}{4} log_{5}5=$
$8 * \frac{1}{4} =2$

Answer 2

To simplify this expression, we can use the following logarithmic identities:

loga(bc) = loga(b) + loga(c) loga(b^c) = c*loga(b)

Using these identities, we can simplify the expression as follows:

25^(log5(sqrt(3)-1)) + 9^(log3(sqrt(3)+1)) * log3(5) / log3(625)

= 5^(2log5(sqrt(3)-1)) + 3^(2log3(sqrt(3)+1)) * log3(5) / log3(5^4)

= 5^(log5(sqrt(3)-1)^2) + 3^(log3(sqrt(3)+1)^2) * log3(5) / 4

= (sqrt(3)-1)^2 + (sqrt(3)+1)^2 * log3(5) / 4

= 2sqrt(3)^2 + 2log3(5) / 4

= 6 + log3(5) / 2

Therefore, the simplified expression is 6 + log3(5) / 2.