Question

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Answer 1

Question:

Find the value of x, if $5^{x-4} =(125)^{2x-1}$

Answer:

$\bigstar{The\:value\:of\:x\:is\:\frac{-1}{5} }$

Explanation:

Given:

• $5^{x-4} =125^{2x-1}$

To Find:

• The value of x

Solution:

$5x^{x-4} =125^{2x-1}$

→ Here 125 can be written as 5³

→ Hence

  $5^{x-4} =5^{(3)^{2x-1} }$

→ We know that $a^{m^{n} } =a^{mn}$

→ Therefore

   $5^{x-4} =5^{6x-3}$

→ Here bases are equal, hence exponents must be equal

   $x-4=6x-3$

   $5x=\:-4+3$

   $x=\:\frac{-1}{5}$

$\boxed{Hence\:the\:value\:of\:x\:is\:\frac{-1}{5} }$

Notes:

→ Some exponential laws

• $a^{m} \times a^{n} =a^{m+n}$

• $\frac{a^{m} }{a^{n} }=a^{m-n}$

• $a^{m^{n} } =a^{mn}$

• $a^{-1} =\frac{1}{a}$

• $a^{0} =1$