Question Detail

$\begin{align} \left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}.\\\text{ What is the value of x ?} \end{align}$

Answer: Option B

Explanation:

$\begin{align}&\left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}\\\\ &\Rightarrow \left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{a}{b}\right)^{-(x-7)}\\\\ &\Rightarrow x - 2 = -(x - 7)\\\\ &\Rightarrow x - 2 = -x + 7\\\\ &\Rightarrow x-2 = -x + 7\\\\ &\Rightarrow 2x = 9\\\\ &\Rightarrow x = \dfrac{9}{2} = 4.5 \end{align}$

1. $\begin{aligned} (1000)^7 \div (10)^{18} = ? \end{aligned}$

10
100
1000
10000

Answer: Option C

Explanation:

$\begin{aligned} = \frac{(10^3)^7}{(10)^{18}} \end{aligned}$

$\begin{aligned} = \frac{(10)^{21}}{(10)^{18}} = 10^3 = 1000 \end{aligned}$

2. $\begin{aligned} x = 3 + 2\sqrt{2}, \text{ then the value of }\\ (\sqrt{x} - \frac{1}{\sqrt{x}}) \end{aligned}$

Answer: Option B

Explanation:

Clue:

$\begin{aligned} (\sqrt{x} - \frac{1}{\sqrt{x}})^2 = x + \frac{1}{x} - 2 \ \end{aligned}$
Now put the value of x to calculate the answer :)

3. $\begin{aligned} \text{If }2x = \sqrt[3]{32}, \text{ then x is equal to} \end{aligned}$

$\begin{aligned} \frac{5}{2} \end{aligned}$
$\begin{aligned} \frac{2}{5} \end{aligned}$
$\begin{aligned} \frac{3}{5} \end{aligned}$
$\begin{aligned} \frac{5}{3} \end{aligned}$

Answer: Option D

Explanation:

$\begin{aligned} = (32)^{\frac{1}{3}}\\ = (2^5)^{\frac{1}{3}}\\ = 2^{\frac{5}{3}}\\ => x= \frac{5}{3} \end{aligned}$

4. $\begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2 \end{aligned}$

Answer: Option C

5. $\begin{aligned} \sqrt{8}^\frac{1}{3} \end{aligned}$

2
4
$\begin{aligned} \sqrt{2} \end{aligned}$
8

Answer: Option C

Explanation:

$\begin{aligned} = ((8)^\frac{1}{2})^\frac{1}{3} = 8^{(\frac{1}{2} \times \frac{1}{3})} \end{aligned}$

$\begin{aligned} = (8)^{\frac{1}{6}} \end{aligned}$

$\begin{aligned} = (2)^{3(\frac{1}{6})} \end{aligned}$

$\begin{aligned} = (2)^{\frac{1}{2}} \end{aligned}$

Question Detail

$\begin{align} \left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}.\\\text{ What is the value of x ?} \end{align}$

1. $\begin{aligned} (1000)^7 \div (10)^{18} = ? \end{aligned}$

2. $\begin{aligned} x = 3 + 2\sqrt{2}, \text{ then the value of }\\ (\sqrt{x} - \frac{1}{\sqrt{x}}) \end{aligned}$

3. $\begin{aligned} \text{If }2x = \sqrt[3]{32}, \text{ then x is equal to} \end{aligned}$

4. $\begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2 \end{aligned}$

5. $\begin{aligned} \sqrt{8}^\frac{1}{3} \end{aligned}$

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Question Detail

(ab)x−2=(ba)x−7. What is the value of x ?\begin{align} \left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}.\\\text{ What is the value of x ?} \end{align}

1. (1000)7÷(10)18=?\begin{aligned} (1000)^7 \div (10)^{18} = ? \end{aligned}

2. x=3+2√2, then the value of (√x−1√x)\begin{aligned} x = 3 + 2\sqrt{2}, \text{ then the value of }\\ (\sqrt{x} - \frac{1}{\sqrt{x}}) \end{aligned}

3. If 2x=3√32, then x is equal to\begin{aligned} \text{If }2x = \sqrt[3]{32}, \text{ then x is equal to} \end{aligned}

4. If 5(a+b)=5×25×125,what is (a+b)2\begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2 \end{aligned}

5. √813\begin{aligned} \sqrt{8}^\frac{1}{3} \end{aligned}

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$\begin{align} \left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}.\\\text{ What is the value of x ?} \end{align}$

1. $\begin{aligned} (1000)^7 \div (10)^{18} = ? \end{aligned}$

2. $\begin{aligned} x = 3 + 2\sqrt{2}, \text{ then the value of }\\ (\sqrt{x} - \frac{1}{\sqrt{x}}) \end{aligned}$

3. $\begin{aligned} \text{If }2x = \sqrt[3]{32}, \text{ then x is equal to} \end{aligned}$

4. $\begin{aligned} \text{If } 5^{(a + b)} = 5 \times 25 \times 125 ,\\ \text{what is }(a + b)^2 \end{aligned}$

5. $\begin{aligned} \sqrt{8}^\frac{1}{3} \end{aligned}$