Solve the given equation for x. $$- 5 = - 6 + 4 e ^ { 7 x }$$
A) $7 e ^ { 4 }$
B) $\frac { e ^ { 4 } } { 7 }$
C) $\frac { \ln 4 } { 7 }$
D) $- \frac { \ln 4 } { 7 }$

Question

Quizplus · Accepted Answer

To solve the equation $-5 = -6 + 4e^{7x}$, first isolate the exponential term:$$4e^{7x} = 1$$$$e^{7x} = \frac{1}{4}$$Taking the natural logarithm of both sides gives:$$7x = \ln\left(\frac{1}{4}\right)$$$$x = \frac{\ln\left(\frac{1}{4}\right)}{7}$$Since $\ln\left(\frac{1}{4}\right) = \ln(4^{-1}) = -\ln(4)$, the solution is:$$x = -\frac{\ln(4)}{7}$$

Solve the Given Equation for X −5=−6+4e7x- 5 = - 6 + 4 e ^ { 7 x }−5=−6+4e7x

Solve the Given Equation for X $- 5 = - 6 + 4 e ^ { 7 x }$