Common and natural logarithms Quiz 1

Question 1

Solve $${(\dfrac{1}{4})^{(5x - 1)}} = 1$$ for $$x$$. Given $$\log 4 = 0.6020$$.

Accepted Answer

$$\dfrac{1}{5}$$

Answer

$$\dfrac{1}{2}$$

Answer

$$\dfrac{1}{3}$$

Answer

$$\dfrac{1}{4}$$

Question 2

Simplify $$4\log {x^{\dfrac{1}{4}}} = \log (8x - 10)$$ and select the correct answer.

Accepted Answer

$$\dfrac{{10}}{7}$$

Answer

$$\dfrac{9}{7}$$

Answer

$$\dfrac{8}{7}$$

Answer

$$0$$

Question 3

Solve $$y = \log \dfrac{{5a}}{{4b}} + \log \dfrac{{3b}}{{4c}} + \log \dfrac{{7c}}{{4a}} + \ln (e)$$ and choose the correct answer.

Accepted Answer

$$1.214$$

Answer

$$4.321$$

Answer

$$9.1$$

Answer

$$0.91$$

Question 4

Solve $$\log 9 + \log (3x - 3) = \log 5 + \log (25x + 30)$$ and mark the correct answer.

Accepted Answer

$$ - 1.806$$

Answer

$$ - 2.806$$

Answer

$$1.806$$

Answer

$$2.806$$

Question 5

Solve $${\log _{16}}({2^x}) = 7$$ and select the correct answer.

Accepted Answer

$$28$$

Answer

$$26$$

Answer

$$27$$

Answer

$$30$$