2 ^ x = 3 ^ (x + 1) solve for x
1 answer:
Answer:
-2.71
Step-by-step explanation:
This exponential equation can be solved by rewriting it so there is only one base, then using logarithms.
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<h3>solve for x</h3>2^x = 3^(x+1) . . . . . given
2^x = 3·3^x . . . . . . eliminate the constant in the exponent
(2/3)^x = 3 . . . . . . . divide by 3^x
x·log(2/3) = log(3) . . . . take logarithms
x = log(3)/log(2/3) ≈ -2.7095113
The value of x is about -2.71.
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<em>Alternate solution</em>
Taking logarithms transforms this exponential equation to a linear equation.
x·log(2) = (x +1)·log(3) . . . . take logs
x(log(2) -log(3)) = log(3) . . . . . . subtract x·log(3)
x = log(3)/(log(2) -log(3)) = log(3)/log(2/3) . . . . . same result as above
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<em>Additional comment</em>
In the attached, we have used a graphing calculator to find the x-intercept of the function f(x) = 0, where f(x) = 2^x -3^(x+1). This is the solution to the given equation.
The applicable rules of logarithms are ...
log(a^b) = b·log(a)
log(a/b) = log(a) -log(b)
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Answer:
The real part is 32, while the imaginary part is 41.9
Step-by-step explanation:
z is a complex number. A complex number is made up of real and imaginary parts.
The real part is the number that stands alone, while the imaginary part is the number that is directly beside the i.
i is actually equal to . There is no solution for that.
Therefore, for the given expression, the real part is 32, while the imaginary part is 41.9.
Note: the imaginary part does not contain i.