Question

What is the value of x in the equation: 2^(3^x) = 10^(6^x) ?

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Answer 1

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  `log\ (log\ 2)/\ log\ 2` or ≈ - 1.73

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Solve in below steps, using log and exponent rules:

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  `2^(3^x)=10^(6^x)` Given
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  `log\ 2^(3^x)=log\ 10^(6^x)` Log both sides
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  `3^x\ log\ 2=6^x\ log\ 10` Log of power rule
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  `3^x\ log\ 2=6^x` log 10 = 1
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  `3^x\ log\ 2=(3*2)^x` Power of the product rule
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  `3^x\ log\ 2=3^x*2^x` Cancel 3ˣ on both sides
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  `log\ 2=2^x` Log both sides
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  `log\ (log\ 2)=x\ log\ 2` Divide both sides by log 2
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  `x=log\ (log\ 2)/\ log\ 2` Answer