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Exponents with Unlike Bases and Same Exponent

Find the valu...

Question

Find the values of x in each of the following :

viii) $(13)^{\sqrt{x}} = 4^{4} - 3^{4} - 6$

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Solution

Given : $(13)^{\sqrt{x}} = 4^{4} - 3^{4} - 6$

$\Rightarrow (13)^{\sqrt{x}} = 256 - 81 - 6$

$\Rightarrow (13)^{\sqrt{x}} = 169$

$\Rightarrow (13)^{\sqrt{x}} = 13^{2}$

On comparing both the sides, we get

$\sqrt{x} = 2$

$\Rightarrow x = 4$

Hence, the value of $x = 4.$

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Similar questions

Q. Find the values of x in each of the following:

(i)

2^{5 x} \div 2 x = \sqrt[5]{2^{20}}

(2^{3})^{4} = (2^{2})^{x}

{(\frac{3}{5})}^{x} {(\frac{5}{3})}^{2 x} = \frac{125}{27}

5^{x - 2} \times 3^{2 x - 3} = 135

2^{x - 7} \times 5^{x - 4} = 1250

{(\sqrt[3]{4})}^{2 x + \frac{1}{2}} = \frac{1}{32}

5^{2 x + 3} = 1

{(13)}^{\sqrt{x}} = 4^{4} - 3^{4} - 6

{(\sqrt{\frac{3}{5}})}^{x + 1} = \frac{125}{27}

Q. Represent each of the following rational numbers on the number line:

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\frac{- 1}{3}

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Find the values of x in each of the following:

$(i) 2^{5 x} \div 2^{x} = \sqrt[5]{2^{20}}$

$(i i) (2^{3})^{4} = (2^{2})^{x}$

$(i i i) {(\frac{3}{5})}^{x} {(\frac{5}{3})}^{2 x} = \frac{125}{27}$

$(i v) 5^{x - 2} \times 3^{2 x - 3} = 135$

$(v) 2^{x - 7} \times 5^{x - 4} = 1250$

$(v i) (\sqrt[3]{4})^{2 x + \frac{1}{2}} = \frac{1}{32}$

$(v i i) 5^{2 x + 3} = 1$

$(v i i i) (13)^{\sqrt{x}} = 4^{4} - 3^{4} - 6$

$(i x) {(\sqrt{\frac{3}{5}})}^{x + 1} = \frac{125}{27}$

Q. Write down the fractional number for each of the following:
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Q. Solve each of the following equation and also check your result in each case:

\frac{3}{4} x + 4 x = \frac{7}{8} + 6 x - 6

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Exponents with Unlike Bases and Same Exponent

Standard VIII Mathematics

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