Question

$solve \: 3 {}^{x} = 5 {}^{x - 2}$
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Answer 1

Answer:

$\boxed{\bf x \ = \ 6.3}$

Step-by-step explanation:

$=>3^{x} =5^{x-2} \\\\ \text{Apply log on both sides,} \\\\ =>log3^x=log5^{x-2} \\\\ \boxed{[loga^n=n \ loga]} \\\\ =>xlog3=(x-2)log5 \\\\ =>xlog3=xlog5-2log5 \\\\ =>2log5=xlog5-xlog3 \\\\=>2log5=x(log5-log3) \\\\ =>x=\frac{2log5}{log5-log3} \\\\ {[log 5=0.69 ]} \\ {[log3=0.477]} \\\\ =>x \simeq 6.3$