Question $e^{1-17 z}=19$

Studdy Solution

STEP 1

1. The equation $e^{(1 - 17z)} = 19$ is exponential.
2. We will need to isolate the variable $z$ by using the natural logarithm, which is the inverse of the exponential function.

STEP 2

1. Take the natural logarithm of both sides to eliminate the exponential.
2. Solve for $z$ .

STEP 3

Take the natural logarithm of both sides of the equation to remove the exponential function:
$e^{(1 - 17z)} = 19$
Apply the natural logarithm:
$\ln(e^{(1 - 17z)}) = \ln(19)$
Using the property of logarithms that $\ln(e^x) = x$ , we simplify the left side:
$1 - 17z = \ln(19)$

STEP 4

Solve for $z$ by isolating it on one side of the equation. First, subtract 1 from both sides:
$1 - 17z = \ln(19)$ $-17z = \ln(19) - 1$
Next, divide both sides by $-17$ to solve for $z$ :
$z = \frac{\ln(19) - 1}{-17}$
The solution for $z$ is:
$z = \frac{\ln(19) - 1}{-17}$

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