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If $153=2(z+z)n$ , then what is the value of $2n(2z)-193$ ?

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Transformations of functions

Full solution

Q. If

153=2(z+z)n

, then what is the value of

2n(2z)-193

?

Simplify the equation: First, let's simplify the given equation $153 = 2(z + z)n$ . Since $2(z + z)$ is the same as $4z$ , we can rewrite the equation as $153 = 4zn$ .
Solve for n: Now, we need to solve for n. To do this, we divide both sides of the equation by $4z$ to isolate $n$ . $\newline$ So, $n = \frac{153}{4z}$ .
Substitute $n$ into expression: Next, we need to find the value of $2n(2z) - 193$ . We already have $n$ expressed in terms of $z$ , so we can substitute $\frac{153}{4z}$ for $n$ in the expression. $\newline$ This gives us $2\left(\frac{153}{4z}\right)(2z) - 193$ .
Simplify the expression: We can simplify the expression by multiplying $2(2z)$ by $153 / (4z)$ . The $2z$ in the numerator and the $z$ in the denominator will cancel out one $z$ , and $2 \times 2$ gives us $4$ , which cancels with the $4$ in the denominator. This simplifies to $2 \times 153 - 193$ .
Calculate $2 \times 153$ : Now, we calculate $2 \times 153$ , which is $306$ . So, we have $306 - 193$ .
Find the final value: Finally, we subtract $193$ from $306$ to find the value of the expression. $\newline$ $306 - 193$ equals $113$ .

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