Solving with logarithms questions with answers

Questions

1. Question 1aˣ = b

   Solve $3^{x} = 40$, giving your answer correct to 3 significant figures.

   Show the worked solution

   1. Step 1: Take lg of both sides; the power law brings the power down$\lg(3^{x}) = \lg 40$$x \lg 3 = \lg 40$
   2. Step 2: Divide by lg a, and work it out$x = \dfrac{\lg 40}{\lg 3}$$= 3.357763\ldots$
   3. Step 3: Round to 3 significant figures$x = 3.36$
2. Question 2aˣ = b

   Solve $3^{x} = 10$, giving your answer correct to 3 significant figures.

   Show the worked solution

   1. Step 1: Take lg of both sides; the power law brings the power down$\lg(3^{x}) = \lg 10$$x \lg 3 = \lg 10$
   2. Step 2: Divide by lg a, and work it out$x = \dfrac{\lg 10}{\lg 3}$$= 2.095903\ldots$
   3. Step 3: Round to 3 significant figures$x = 2.10$
3. Question 3a^(px + q) = b

   Solve $7^{2x} = 15$, giving your answer correct to 3 significant figures.

   Show the worked solution

   1. Step 1: Take lg of both sides; the power law brings the power down$\lg(7^{2x}) = \lg 15$$(2x) \lg 7 = \lg 15$
   2. Step 2: Divide by lg a, and work it out$2x = \dfrac{\lg 15}{\lg 7}$$= 1.391663\ldots$
   3. Step 3: Solve, then round to 3 significant figures$x = 0.696$
4. Question 4a^(px + q) = b

   Solve $5^{2x} = 10$, giving your answer correct to 3 significant figures.

   Show the worked solution

   1. Step 1: Take lg of both sides; the power law brings the power down$\lg(5^{2x}) = \lg 10$$(2x) \lg 5 = \lg 10$
   2. Step 2: Divide by lg a, and work it out$2x = \dfrac{\lg 10}{\lg 5}$$= 1.430677\ldots$
   3. Step 3: Solve, then round to 3 significant figures$x = 0.715$