solve the equation log(base16)(3x-1)= log(base4)(3x)+log(base4)0.5?

Anish Buchanan

Anish Buchanan

Answered question


solve the equation log(base16)(3x1)=log(base4)(3x)+log(base4)0.5?

Answer & Explanation



Skilled2021-03-08Added 105 answers

log[4](16)log[16]4=1 where [] denotes base, is an example of a fundamental rule in logarithms: log[a](b)log[b](a)=1, so, since log[4](16)=2log[4]4=2,log[16]4=12, or, alternatively, log[16]4=log[16]1612=12log[16]16=12.
Also, log[a](x)=log[b]xlog[b]
(a). log[16](3x1)=log[4](3x)+log[4](0.5)2log[4](3x1)=log[4](3x0.5). We can equate the logs: (3x1)2=3x29x26x+1=3x218x212x3x+2=0
From this x=23or16. Substitute these values in the original equation: 0=1212. The value 16 cannot be used because it would require the log of a negative number so the only solution is Lx=23

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