Question

Solve the following exponential equations-
1) (5/3)³⁰_÷ (25/9)^x+4_× (5/3)¹²₌ 1
2) 5^2x+1 ÷25 = 125

Answer 1

Dear student
$$\begin{gathered} 2) \\ {5}^{2x+1}÷25=125 \\ \Rightarrow 5^{2x+1}÷5^2=5^3 \\ \Rightarrow 5^{2x+1}\times \frac{1}{5^2}=5^3 \\ \Rightarrow 5^{2x+1-2}=5^3\left[As\frac{a^m}{a^n}=a^{m-n}\right] \\ \Rightarrow 5^{2x-1}=5^3 \\ Oncomparingthepowers,weget \\ \Rightarrow 2x-1=3 \\ \Rightarrow 2x=4 \\ \Rightarrow x=2 \end{gathered}$$
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