Question

7^5x+2=125. Equação exponencial

Answer 1

$\mathsf{7^{5x+2}=125}\\ \mathsf{\log(7^{5x+2})=\log(125)}\\ \mathsf{\log(7)^{5x+2}=\log(5)^3}\\ \mathsf{(5x+2)\cdot\log(7)=3\cdot\log(5)}\\\\ \mathsf{\log(5)=0,699~~e~~\log(7)=0,845}\\\\ \mathsf{0,845\cdot(5x+2)=3\cdot0,699}\\ \mathsf{4,225x+0,97=2,097}\\ \mathsf{4,225x=2,097-0,97}\\ \mathsf{4,225x=1,127}\\\\ \mathsf{x= \dfrac{1,127}{4,225} }\\\\\\ \Large\boxed{\mathsf{x\approx0,2667}}$