Find the value of x in the following- 35x-532x-12527

We have (35)^x.(53)^2x=12527 #160; #160; [∵(ab)^n=(ba)^ n] ⇒(53)^ x.(53)^2x=(53)^3 #160; ⇒(53)^ x+2x=(53)^3 #160; ⇒(53)^x=(53)^ ...

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Exponential Representation for Irrational Numbers

Find the valu...

Question

Find the value of x in the following:
$(\frac{3}{5})^{x} . (\frac{5}{3})^{2 x} = \frac{125}{27}$

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

Find the values of x in each of the following:

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

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

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

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

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

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

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

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

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

Q6. Find the value of x:

a) (125/ 8) X (125/ 8)^x = (5/2)¹⁸

b) 3^{2x + 1} / 9 = 27

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

x

(\frac{125}{27}) \times (\frac{125}{27})^{x} = (\frac{5}{3})^{18}

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