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❓ Question Find the value of 81 1 log ⁡ 5 3 + 27 log ⁡ 9 36 + 3 4 log ⁡ 7 9 . 81^{\frac{1}{\log_5 3}} +27^{\log_9 36} +3^{\frac{4}{\log_7 9}}. ✍…

❓ Question If m = log ⁡ 245 175 , n = log ⁡ 1215 875 , m=\log_{245}175,\qquad n=\log_{1215}875, find the value of m − n 1 − m n . \frac{m-n}{1-mn}…

❓ Question If log ⁡ 8 ( 8 x 2 ) ( log ⁡ 8 x ) 2 = 3 , \frac{\log_{8}\left(\frac{8}{x^{2}}\right)} {\left(\log_{8}x\right)^2}=3, find the product …

❓ Question Given e 2 ⋅ x ln ⁡ x = x 3 , e^2\cdot x^{\ln x}=x^3, where x > β , α m = β n , x>\beta,\qquad \alpha^m=\beta^n, and m , n m,n …

❓ Question If ∣ x + y ∣ + ∣ x − y ∣ = 2 ∣ x ∣ |x+y|+|x-y|=2|x| and ∣ x + 1 ∣ + ∣ 5 − x ∣ = 6 , |x+1|+|5-x|=6, then find the possible values of x…

❓ Question Let y = [ x ] y=[x] be the Greatest Integer Function (GIF), and y = { x } y=\{x\} be the Fractional Part Function. The graph of y = …

❓ Question Given f ( x ) = log ⁡ ( 1 + x 1 − x ) , f(x)=\log\left(\frac{1+x}{1-x}\right), find f ( 3 x + x 3 1 + 3 x 2 ) . f\left(\frac{3x+x^3}{…