Question

Need help with this word problem please.

Answer 1

Use log laws on the right hand side to combine them first.

Then put both sides to the power of 10.

Answer 2

\(\bf log(y)=log(b)-k\cdot log(x)\implies log_{10}(y)=log_{10}(b)-k\cdot log_{10}(x)\\ \quad \\
\textit{log cancellation rule of }\quad a^{log_ax}=x\qquad thus\\ \quad \\
log_{10}(y)=log_{10}(b)-k\cdot log_{10}(x)\ \quad \\
\implies \Large 10^{log_{10}(y)}=10^{log_{10}(b)-k\cdot log_{10}(x)}\\ \quad \\
\implies y=?\)

Answer 3

just put everything under 10 log 10 (y)?

Answer 4

You can combine the logs on the right first, to simplify a bit, but not necessary.

Answer 5

What would the final answer be with them combined then?

Answer 6

Try it using log laws.

\[\Large y \log x = \log x^y\]

\[\Large \log a - \log b = \log (a/b)\]

Answer 7

Use both of those on the right.