2^x+20=15+3^x

A)1
B)16
C)-5
D)25

I chose c but i got it wrong i am having a problem understanding it.

Let me rewrite the question in a more standard format.

2* sqrt(x)+20=15 + 3*sqrt(x)

where * means multiply, and sqrt means the square root. Your use of ^ for square root is unusual, normally, we use the carat sign, ^, as an exponent..for instance, 2 cubed will be 2^3.

Ok, your problem.
2* sqrt(x)+20=15 + 3*sqrt(x)
gather your terms..
2* sqrt(x)- 3*sqrt(x) =15 - 20
- sqrt(x)=-5
square both sides...
x=25

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To solve the equation 2^x + 20 = 15 + 3^x, we gather like terms and try to isolate the variable x on one side of the equation.

First, we can rewrite the equation in a more standard format:

2^x - 3^x = 15 - 20

Next, we simplify the equation. Since the bases of the exponents are different, we cannot combine them directly. Instead, we can rewrite the equation using a common base. Let's rewrite 3^x as (2^x)^(log2(3)):

2^x - (2^x)^(log2(3)) = -5

Using the property of exponentiation that states (a^b)^c = a^(b*c), we get:

2^x - 2^(x*log2(3)) = -5

Now, we can notice that 2^x is present in both terms on the left side of the equation. We can factorize it out:

2^x * (1 - 2^(log2(3))) = -5

Simplifying the expression in parentheses, we have:

2^x * (1 - 3) = -5

2^x * (-2) = -5

Dividing both sides of the equation by -2, we get:

2^x = 5/2

Finally, to solve for x, we need to take the logarithm of both sides of the equation. Since we have a base 2, we can use the logarithm property log(a^b) = b * log(a):

x * log2(2) = log2(5/2)

Simplifying further, we have:

x = log2(5/2)

Using a calculator to evaluate log2(5/2), we find that x is approximately 0.321928.

Based on the options available (A, B, C, D), none of them represent the correct answer. Therefore, it seems like this equation may not have a solution among the given options.