Domanda del libro di testo
13. For what x>0 does x^(x^x) = (x^x)^x? Give reasons for your answer.
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0. Functions
Exponential & Logarithmic Equations
Scelta multipla
Solve the exponential equation.
A
B
C
D
Guida verificata passo dopo passo1
Start by isolating the exponential term. Divide both sides of the equation \(2 \cdot 10^{3x} = 5000\) by 2 to get \(10^{3x} = 2500\).
To solve for \(x\), take the logarithm of both sides. Use the common logarithm (base 10) for simplicity: \(\log(10^{3x}) = \log(2500)\).
Apply the logarithmic identity \(\log(a^b) = b \cdot \log(a)\) to the left side: \(3x \cdot \log(10) = \log(2500)\).
Since \(\log(10) = 1\), the equation simplifies to \(3x = \log(2500)\).
Finally, solve for \(x\) by dividing both sides by 3: \(x = \frac{\log(2500)}{3}\).
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