Solve 4log₂(2)+log₂(x)=3
First, we should look at the laws of logarithms.logax+logay=logaxylogax-logay=loga(x/y)klogax=logaxkWe can see that laws 1 and 3 might be helpful, so we simplify our equation.log224 +log2x=3log224x=3log216x=3Next, we just have to rearrange for x. The inverse of a logarithm is an exponential, so put each side of the equation as a power of 2 (as this is the base of the logarithm). This allows us to remove the logarithm and exponential from one side and we just have to divide by 16 after this.2log16x=2316x=8x=1/2
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