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❓ Question Given 2 x + y = 6 y , 3 x − 1 = 2 y + 1 , 2^{x+y}=6^y,\qquad 3^{x-1}=2^{y+1}, where x = x 1 , y = x 2 . x=x_1,\qquad y=x_2. Find log…

❓ Question Find the number of solutions of ∣ 2 x − 1 ∣ + ∣ 4 − 2 x ∣ < 3. |2^x-1|+|4-2^x|<3. ✍️ Solution Let t = 2 x ( t > 0 ) . t=2^…

❓ Question If f ( x ) = x 2 + 2 x + 1 − x 2 − 2 x + 1 , f(x)=\sqrt{x^2+2x+1}-\sqrt{x^2-2x+1}, find f ⁣ ( − 5 4 ) + f ⁣ ( 3 4 ) + f ⁣ ( 7 4 ) …

❓ Question Evaluate 81 1 log ⁡ 3 5 + 27 log ⁡ 36 log ⁡ 9 + 3 4 log ⁡ 7 9 . 81^{\frac{1}{\log_3 5}} + 27^{\frac{\log 36}{\log 9}} + 3^{\frac{4}{\l…

❓ Question If log ⁡ ( x + 3 ) ( x 2 − x ) < 1 \log_{(x+3)}(x^2-x)<1 is satisfied for x ∈ ( a , b ) , x\in(a,b), then find the value of a …

❓ Question Let 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-m…

❓ Question Find the unique value of x x satisfying 4 x − 3 x + 1 2 = 3 x + 1 2 − 2 2 x − 1 . 4^x-3^{x+\frac12}=3^{x+\frac12}-2^{\,2x-1}. ✍️ S…