Quiz about Logarithms Laws and Equations

Question 1

Simplify $$\lg9+\lg7$$ .

Accepted Answer

$$\lg63$$

Answer

$$\lg16$$

Answer

$$\lg2$$

Question 2

Express as a single logarithm.

$$\log_aa^4+\lg4$$

Accepted Answer

$$\lg40000$$

Answer

$$\lg400$$

Answer

$$\lg4000$$

Question 3

Express as a single logarithm.

$$\log_bb\left(\sqrt[3]{b}\right)-\ln b$$

Accepted Answer

$$\ln\left(\frac{\sqrt[3]{e^4}}{b}\right)$$

Answer

$$\ln\left(\frac{\sqrt[]{e^4}}{b}\right)$$

Answer

$$\ln e^4b$$

Question 4

Without using a calculator, evaluate each of the following.

$$\log_419 imes\log_{19}64$$

Accepted Answer

3

Answer

2

Answer

6

Question 5

Without using a calculator, evaluate the following.

$$\ln\sqrt[]{e}-\lg\sqrt[3]{10}$$

Accepted Answer

$$\frac{1}{6}$$

Answer

6

Answer

3

Question 6

Given that $$\log_9x=p$$ , express each of the following in terms of p.

(a) $$\log_981x^3$$

Accepted Answer

$$2+3p$$

Answer

$$2p+3$$

Answer

$$p+3$$

Question 7

Given that $$\log_9x=p$$ , express each of the following in terms of p.

(b) $$\log_9\left(\frac{1}{x}\right)$$

Accepted Answer

$$-p$$

Answer

$$\frac{1}{p}$$

Answer

$$p$$

Question 8

Given that $$\log_9x=p$$ , express each of the following in terms of p.

(c) $$\left(\log_3\sqrt[]{3x}\right)^2$$

Accepted Answer

$$\frac{1}{4}\left(1+2p\right)^2$$

Answer

$$\frac{1}{2}\left(1+2p\right)^4$$

Answer

$$4\left(1+2p\right)^2$$

Question 9

Given that $$\log_9x=p$$ , express each of the following in terms of p.

(d) $$x^2$$

Accepted Answer

$$9^{2p}$$

Answer

$$9^p$$

Answer

$$2p$$

Question 10

Solve the equation

$$\log_7\left(x+2\right)+\log_7\left(x+5\right)=\log_72+\log_7\left(x+3\right)$$

Accepted Answer

$$-1$$

Answer

$$1$$

Answer

$$1.5$$

Question 11

Solve the following equation.

$$\log_4\left(x+10\right)-\log_4\left(x-2\right)=\log_4\left(x+3\right)$$

Accepted Answer

$$4$$

Answer

$$2$$

Answer

$$\frac{1}{2}$$

Question 12

Solve the following equation.

$$2\log_5x-\log_5\left(x+100\right)=1$$

Accepted Answer

$$25$$

Answer

$$5$$

Answer

$$125$$

Question 13

Solve the following equation.

$$\ln6x=\frac{1}{2}\ln\left(23x^2+1\right)-\ln2$$

Accepted Answer

$$\frac{1}{11}$$

Answer

$$11$$

Answer

$$-\frac{1}{11}$$

Question 14

Solve the following equation

$$\log_x243=4+\log_x3$$

Accepted Answer

$$3$$

Answer

$$\frac{1}{3}$$

Answer

$$6$$

Question 15

Solve the following equation

$$\lg x+54\log_x10=15$$

Accepted Answer

$$10^6\ or\ 10^9$$

Answer

$$10^7\ or\ 100$$

Answer

$$1000\ or\ 10^5$$

Logarithms Laws and Equations

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