Question

find x :
Maths - logarithms​

Answer 1

Answer:

x = 10

Step-by-step explanation:

${5}^{ log(x) } + {3}^{ log(x) } = {3}^{ log(x) + 1} - {5}^{ log(x - 1) } \\ = > {5}^{ log(x) } + {5}^{ log(x ) - 1 } = {3}^{ log(x) + 1 } - {3}^{ log(x) } \\ = > {5}^{ log(x) } + {5}^{ log(x) } \times \frac{1}{5} = 3 \times {3}^{ log(x) } - {3}^{ log(x) } \\ = > {5}^{ log(x) }(1 + \frac{1}{5} ) = {3}^{ log(x) }(3 - 1) \\ = > {5}^{ log(x) } \times \frac{6}{5} = {3}^{ log(x) } \times 2 \\ = > { (\frac{5}{3} )}^{ log(x) } = 2 \times \frac{5}{6} \\ = > { (\frac{5}{3} )}^{ log(x) } = \frac{5}{3} \\ = > log(x) = 1 \\ = > x = 10$