# Additional Math – Logarithms – Show that the expression equals to 12

Change all log to base 10 (lg). Use the change of base formula.

$latex \displaystyle \frac{{\lg 7}}{{\lg 2}}\times \frac{{\lg 8}}{{\lg 3}}\div \frac{{\lg \sqrt{7}}}{{\lg 9}}$

$latex \displaystyle \frac{{\lg 7}}{{\lg 2}}\times \frac{{\lg {{2}^{3}}}}{{\lg 3}}\div \frac{{\lg {{7}^{{\frac{1}{2}}}}}}{{\lg {{3}^{2}}}}$

Use the formula logabc= c logab. Simplify the expression.

$latex \displaystyle \frac{{\lg 7}}{{\lg 2}}\times \frac{{3\lg 2}}{{\lg 3}}\div \frac{{\frac{1}{2}\lg 7}}{{2\lg 3}}$

$latex \displaystyle\frac{{3\lg 7}}{{\lg 3}}\div \frac{{\frac{1}{2}\lg 7}}{{2\lg 3}}$

$latex \displaystyle\frac{{3\lg 7}}{{\lg 3}}\times \frac{{2\lg 3}}{{\frac{1}{2}\lg 7}}$

$latex \displaystyle\frac{3}{1}\times \frac{2}{{\frac{1}{2}}}$

12 (Shown)

Normally student will change the expression to the same base number. But it will be difficuil for the bove question. A better solution is to change all to base 10 (lg), the cancel out the common logs. You may also change to ln (loge) instead of lg., the answer will still be the same.

Additional Math amath Tuition at Woodlands. Students from Yew Tee, Choa Chu Kang, Yishun & Sembawang Welcome.

## Share:

### Math – Statistics – 1st Quartile, Median and 3rd Quartile Ungroup Data

The above two diagrams show you how to find the 1st quartile, median (2nd Quartile) and the 3rd quartile ungroup

### Additional Math – Differentiation – Quotient Rule (Challenging)

Differentiate $latex \displaystyle\ y=\frac{{{{x}^{2}}\sqrt{{x+1}}}}{{x-1}}$ with respect to x. Simplify the Numerator (otherwise you need to use both quotient rule for

### Additional Math – Binomial theorem – Using Normal Expansion vs Binomial Theorem

The above video shows  two method of expanding the  expression; using the algebraic expansion (rainbow method) versus the binomial theorem.