Question

Solve the exponential equation in terms of natural logarithms

Answer 1

\[4^{1-x} = 5\]

So I took the natural log of both sides:
\[\ln (4^{1-x}) = \ln(5)\]

Moved the exponent to the front:
\[(1-x)\ln(4) = \ln(5)\]

divided by ln(4)
\[(1-x) = \frac{ \ln(5) }{ \ln(4) }\]

Answer 2

Where do I go from here?

Answer 3

So wouldn't the answer just be
\[1-\frac{ \ln5 }{ \ln4 }\]

Answer 4

why does the one go in front?

Answer 5

\[1-x=\frac{ \ln5 }{ \ln4 }\]
\[-x=-1+\frac{ \ln5 }{ \ln4 }\]

Answer 6

So
\[x=1-\frac{ \ln5 }{ \ln4 }\]