Solving Logarithms

Match the following:

Rewrite the following in the form $$\log\left(c\right)$$

Solve the following

$$\log_3\left(x+3\right)+2\log_3\left(2\right)=3$$

(number only)

Solve $$5\log_x16=10$$ (number only)

On the Richter Scale, the Magnitude $$R$$ of an earthquake with Intensity $$I$$ is measured by

$$R=\log_{10}\left(\frac{I}{I_o}\right)$$

Where $$I_o=1$$ is the minimum intensity used for comparison.

Find the magnitude of an earthquake that has an intensity of 325,000 (round to the nearest tenth)

Chemists use the formula $$pH=-\log\left(H^+\right)$$ , where $$H^+$$ is the hydrogen ion concentration, to determine the acidity or alkalinity of a substance.

What would be the pH of a solution with a concentration of $$\left[H^+\right]=0.0003$$ (round to the nearest tenth)

Chemists use the formula $$pH=-\log\left(H^+\right)$$ , where $$H^+$$ is the hydrogen ion concentration, to determine the acidity or alkalinity of a substance.

What would be the concentration of $$H^+$$ if the pH was 1.2? (round to the nearest thousandth)

If a sample of curium-240 has a half life of 27 days, and originally starts with a mass of 25g. How long will it take for the sample to break down until only 5g remain? (round to the nearest day)

If a bacterial colony doubles every 8 hours, and originally had a mass of 0.2mg. How long would it take for the colony to reach 1.5mg? (round to the nearest hour)