Question

please solve using natural log: 5^x-1(times by) 3^x+2=10

Answer 1

well if you take the log of each you get

\[\ln(5^{x -1} \times 3^{x + 2}) = \ln(10)\]

then applying the log laws for multiplication and powers you get

\[(x -1)\ln(5) + (x + 2) \ln(3) = \ln(10)\]

which becomes

\[x(\ln(5) + \ln(3)) - \ln(5) + 2\ln(3) = \ln(10)\]

so it simplifies to

\[x(\ln(5) + \ln(3)) = \ln(10) + \ln(5) - \ln(3)\]

now just solve for x