Pregunta
\( \left. \begin{array} { l | l } { .2 .2 } & { 2 ^ { x } = 64 } \\ \hline \end{array} \right. \)
Ask by Garrett Willis. in South Africa
Jan 22,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( x = 6 \)
Solución
The given equation is \(2^x = 64\).
To solve for \(x\), we can use the property of exponents that states if \(a^b = c\), then \(b = \log_a(c)\).
Therefore, we can rewrite the equation as \(x = \log_2(64)\).
Now, we can calculate the value of \(x\) using the logarithm base 2 of 64.
Calculate the value by following steps:
- step0: Calculate:
\(\log_{2}{\left(64\right)}\)
- step1: Write in exponential form:
\(\log_{2}{\left(2^{6}\right)}\)
- step2: Simplify the expression:
\(6\)
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución The Deep Dive
To solve the equation \( 2^x = 64 \), we can express 64 as a power of 2. Since \( 64 = 2^6 \), we rewrite the equation as \( 2^x = 2^6 \). By equating the exponents, we find that \( x = 6 \). So, the solution to the equation is \( x = 6 \). Isn't it fascinating how exponents work? They form the backbone of exponential growth in many situations, including population modeling and finance! From baking—where doubling a recipe can necessitate understanding exponential increases—to computer science, where data structures can require efficient algorithms based on powers of 2, these concepts seep into everyday life in surprising ways!
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
