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surfy2455
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With equations like these, where the variable appears in the exponent and outside the exponent, there's not usually an easy way to solve the equations using algebra. I think your best bet is either to treat each side of the original equation as a function, and graph it, and then look for intersections of the two graphs.surfy2455 said:Homework Statement
200n = 2^(n-1) find n
The Attempt at a Solution
200n = 2^(n-1)
200 = 2^(n-1)/n
ln(200) = ln(2^(n-1)/n)
ln(200) = ln(2^(n-1)) - ln(n)
ln(200) = (n-1) * ln(2) - ln(n)
5.3 = .7n - .7 - ln(n)
6 = .7n -ln(n)
This is where I get stuck, not sure if this is the right approach.
Homework Statement
6n^2 = 2^(n-1) find n
The Attempt at a Solution
6n^2 = 2^(n-1)
ln(6n^2) = ln(2^(n-1))
2 * ln(6n) = (n-1) * ln(2)
2 * ln(6n) = .7n -.7
Stuck again
Mark44 said:I see that you started another thread here - https://www.physicsforums.com/showthread.php?t=720463. That gives some context to the problem. For one thing, n is an integer, as it represents the number of steps in an algorithm, or something related to that.
With that context, all you need to do is to find numbers n and n + 1 that straddle the exact solution. In other words, when you substitute that value of n in the equations, the left side is smaller than the right side. When you substitute n + 1, the left side is larger than the right side.
An exponential equation is an equation in which a variable appears in the exponent. It can be written in the form y = abx, where a and b are constants and x is the variable.
To solve an exponential equation, you can use logarithms or take the logarithm of both sides of the equation. You can also use the property of logarithms that states that logb(ax) = xlogb(a) to solve for the variable.
An exponential equation is an equation in which a variable appears in the exponent, while a logarithmic equation is an equation in which a variable appears in the logarithm. The two are inverse operations of each other and can be used to solve for the variable in the other equation.
Exponential equations are used to model growth and decay in various fields, such as population growth, compound interest, and radioactive decay. They are also used in physics, chemistry, and biology to describe exponential processes.
Yes, exponential equations can have negative exponents. A negative exponent indicates that the base is being raised to a power that is less than 1. In this case, the result is a fraction or decimal. Negative exponents can also be rewritten as positive exponents using the rule a-n = 1/an.