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physstudent1
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Homework Statement
2^x =x^3
show that the equation has at least two solutions.
Homework Equations
The Attempt at a Solution
I got xln2=3lnx but I don't know what I could do from here
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An exponential function is a mathematical function in the form of f(x) = a^x, where a is a constant and x is a variable. It is characterized by a rapidly increasing or decreasing graph and is commonly used to model growth or decay.
To graph an exponential function, you can create a table of values by plugging in different values for x and solving for f(x). Then, plot these points on a coordinate plane and connect them with a smooth curve. Alternatively, you can use the properties of exponential functions to make a sketch of the graph.
To solve an exponential equation, you can use logarithms. If the equation is in the form a^x = b, you can take the log of both sides using the base a. If the equation is in the form a^x = c, you can take the log of both sides using any base and then use the change of base formula to solve for x.
Exponential functions are commonly used to model population growth, compound interest, radioactive decay, and the spread of diseases. They can also be used in fields such as physics, biology, and finance to describe processes that involve rapid growth or decay.
Exponential functions have a variable in the exponent, while linear functions have a variable in the base. This results in a different rate of change for each function. Exponential functions also have a non-constant rate of change, while linear functions have a constant rate of change.