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First, we take logs of both sides: log(5^(2x+1))=log(7) Now, using the 3rd law of logs (index rule; using the power as the coefficient), we get: (2x+1)log(5)=log(7) i.e. 2x+1 = (log(7))/(log(5)) = 1.20906...

This can be proven by understanding tan(x) and it's inverse as functions, using implicit differentiation, subsitution and by recognising trigonometric identities (or being able to prove them from first pr...

Firstly write out the equation x² - 9x + 20 = 0. The aim is to find two numbers that multiply to make 20 and add up to make -9. Look at the constant without any x's , in this case it is 20. We ...

It would be worked out by adding 4+6+10 to get 20 and then it would be number of yellow balls over total number of balls which would be 10/20. Depending on ability this may then be simplified down to 1/2....

Perimeter of a rectangle is the sum of all the sides. Therefore: 2(4+3x) + 2(x+6) = 32. Then, you expand: 8+6x+2x+12=32. Then, 8x+20=32. Finally, 8x=12, meaning that x=3/2.