exam Maths Puzzle Numerical Ability

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how can you solve the first one ? my 1st try resulted to x=2 and x=1.

about the last 2, how can you express into loga

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exam Other Question

Did I do this problem correctly?

solve by using quadratic formula

x^2-4X-60=0

x=1(-4)+- radical 4^2+4*1*(-60)/2*1
Solve. 4^2=x^2+a+1t