A) no solution
B) one solution
C) two solutions
D) more than two solutions
Correct Answer: B
Solution :
\[f(x)={{\left( \frac{3}{5} \right)}^{x}}+{{\left( \frac{4}{5} \right)}^{x}}-1\] Put f(x) = 0 \[\Rightarrow \]\[0={{\left( \frac{3}{5} \right)}^{x}}+{{\left( \frac{4}{5} \right)}^{x}}-1\] \[\Rightarrow \]\[{{\left( \frac{3}{5} \right)}^{x}}+{{\left( \frac{4}{5} \right)}^{x}}=1\] \[\Rightarrow \]\[{{3}^{x}}+{{4}^{x}}={{5}^{x}}\] For\[x=1\] \[{{3}^{3}}+{{4}^{3}}=91<{{5}^{3}}\] Only for x = 2, equation (1) Satisfy So, only one solution (x = 2)
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