Question

Express 2lg3√x - lg 4/3x^2 + 1og base 100 4x^3 in the form a lg x = lg b where a and b are constants

Answer 1

\[2\log_{} 3\sqrt{x}-\log_{} \frac{4}{3x^2}+\log_{100} 4x^3\]Is this correct?

Answer 2

answer given is 9/2lg x + lg 27/2

Answer 3

did I get the expression you're supposed to work with correctly though?

Answer 4

yup

Answer 5

ok. look at the first term 2log (3 sqrt x). Bring the coefficient into the log. It becomes an exponent. We get:\[2\log_{} 3\sqrt{x}=\log_{} (3\sqrt{x})^2=\log_{} 9x\]

Answer 6

Now we can bring together the first two terms:\[\log_{} 9x-\log_{} \frac{4}{3x^2}=\log_{} \frac{9x}{\frac{4}{3x^2}}=\log_{} \frac{27x^2}{4}\]

Answer 7

ooops, should be x^3 not x^2

Answer 8

Now, we need to express the log base 100 as a log base 10 in order to simplify this one. \[\log_{100} 4x^3=\frac{\log_{10} 4x^3}{\log_{10} 100}=\frac{\log_{10} 4x^3}{2}\]

Answer 9

so,