Question

log x - log(x+14) = -1 can anyone help me solve please

Answer 1

Rewrite the left side as a logarithm:

log (x/(x+14)

Answer 2

Becuase log (A/B) = log A - log B

Answer 3

So your equation is log(x/(x+14)) = -1

Answer 4

To solve that, write that equation in exponential form..and you'll almost be done.

Answer 5

\(\bf log x - log(x+14) = -1 \implies log_{10} x - log_{10}() = -1 \\ \quad \\
log_{10}\left(\cfrac{x}{x+14}\right)=-1\\ \quad \\
\textit{log cancellation rule of}\quad a^{log_ax}=x\\ \quad \\
\large 10^{log_{10}\left(\frac{x}{x+14}\right)}=10^{-1}\implies \cfrac{x}{x+14}=10^{-1}\)

Answer 6

hmm I have a typo.... .. well. \(\bf log( x) - log(x+14) = -1 \implies log_{10} x - log_{10}(x+14) = -1 \\ \quad \\
log_{10}\left(\cfrac{x}{x+14}\right)=-1\\ \quad \\
\textit{log cancellation rule of}\quad a^{log_ax}=x\\ \quad \\
\large 10^{log_{10}\left(\frac{x}{x+14}\right)}=10^{-1}\implies \cfrac{x}{x+14}=10^{-1}\)