Question 54

If $$\log_{2}[3+\log_{3} \left\{4+\log_{4}(x-1) \right\}]-2=0$$ then 4x equals

Correct Answer: 5

Solution

We have :
$$\log_2\left\{3+\log_3\left\{4+\log_4\left(x-1\right)\right\}\right\}=2$$
we get $$3+\log_3\left\{4+\log_4\left(x-1\right)\right\}=4$$
we get $$\log_3\left(4+\log_4\left(x-1\right)\ =\ 1\right)$$
we get $$4+\log_4\left(x-1\right)\ =\ 3$$
$$\log_4\left(x-1\right)\ =\ -1$$
x-1 = 4^-1
x = $$\frac{1}{4}+1=\frac{5}{4}$$
4x = 5

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