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Solve 4log₂(2)+log₂(x)=3

First, we should look at the laws of logarithms.log_ax+log_ay=log_axylog_ax-log_ay=log_a(x/y)klog_ax=log_ax^kWe ca...

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Prove that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.

A problem of this nature seems complex at first until you break it down and see what it is really asking you to find. We can represent two consecutive integers as x and x + 1. The problem asks us to prove...

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Simplify 3 × a × 3 × a

The question asks you to simplify an expression, this means we need to write it with as few symbols and numbers as we can.Multiplication is commutative, this means that it doesn't matter which order we do...

Answered by Rob G. • Maths tutor

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Simplify 7 × e × f × 8

Always do the numbers first before dealing with the letters. We move the numbers to one side, and the letters to the other. (7 x 8) x e x f -> I have enclosed the

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Solve the integral int(sin^2(x))dx

Knowing that 1-2sin²(x) = cos(2x), substitute sin²(x) as: sin²(x) = (1-cos(2x))/2Use the linearity of the integral to split it into: Int(1/2) - Int(cos(2x)/2)dxWhich is in...

Answered by Maks M. • Maths tutor

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