Question

Log 2 x + log 4 x + log8 x = 5 Решите пожалуйста!!!!!)))

Answer 1

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Answer 2

Solving the Equation log2(x) + log4(x) + log8(x) = 5

To solve the equation log2(x) + log4(x) + log8(x) = 5, we can use logarithmic properties to simplify the equation and find the value of x.

Let's start by applying the logarithmic property that states loga(b) + loga(c) = loga(b * c). Using this property, we can rewrite the equation as a single logarithm:

log2(x) + log4(x) + log8(x) = log2(x) + log(2^2)(x) + log(2^3)(x) = log2(x) + 2log2(x) + 3log2(x) = log2(x) + 2log2(x) + 3log2(x) = 6log2(x) = 5

Now, we can simplify the equation further:

6log2(x) = 5

To isolate the logarithm, we divide both sides of the equation by 6:

log2(x) = 5/6

To convert the logarithmic equation into an exponential equation, we can rewrite it as:

x = 2^(5/6)

Therefore, the solution to the equation log2(x) + log4(x) + log8(x) = 5 is x = 2^(5/6).

Please note that the above solution is based on the given equation and the application of logarithmic properties.