Question

if 3 power x us equal to 5 power x-2​

Answer 1

Answer:

3x=5x-2x

hope this helps you

Answer 2

Correct question :

If 3ˣ = 5ˣ⁻² , then find the value of x

Answer:

$\bf x= \dfrac{\log 25}{\log \dfrac{5}{3}}$

Step-by-step explanation:

$\sf 3^x=5^{x-2}$

Applying log on both sides,

$\sf \log 3^x= \log 5^{x-2} \\\\ x\log 3 = (x-2)\log5 \: \bf [ \log a^n=n \log a]\\\\ x \log 3 = x \log5 - 2 \log 5 \\\\ x \log 3 =x \log 5-log 5^2 \\\\ x \log 3 =x \log 5-\log 25 \\\\ \log 25=x \log 5 - x \log 3 \\\\ \log 25 =x( \log 5 - \log 3) \\\\ \log 25=x( \log \dfrac{5}{3}) \quad \bf [\log m - \log n = \log \dfrac{m}{n}]\\\\ \underline{ \boxed{\sf x= \dfrac{\log 25}{\log \dfrac{5}{3}}}}$

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LOGARITHM FORMULAS :

$\boxed{\boxed{\begin{minipage}{5cm}\displaystyle\circ\sf\ log_a \ 1= 0\\\\\circ \ log_a \ a = 0 \\\\\circ \ log_a \ \frac{m}{n}= \ log_a \ m - log_a \ n \\\\\circ \ log_a \ (mn) = \ log_a \ m + log_a \ n \\\\\circ \ log_a \ x^n = n log_a \ x\\\\\circ \ log_a \ c = \dfrac{1}{ log_c \ a} \\\\\circ \ a^{log_a x} = x \\\\\circ \ log_e \ x= ln \ x\end{minipage}}}$