Solve for x: 5^{log x} + 3^{log x} = 3^{log x + 1} - 5^{log x - 1}.

Question

KnowledgeBoat · Accepted Answer

Given, 5^{log x} + 3^{log x} = 3^{log x + 1} - 5^{log x - 1} ⇒ 5^{log x} + 3^{log x} = 3^{log x}.3¹ - 5^{log x}.5^-1 ⇒ 5^{log x} + 5^{log x}.5^-1 = 3^{log x}.3¹ - 3^{log x} ⇒ 5^{log x}(1 + 5^-1) = 3^{log x}(3 - 1) ⇒ 5^{log x} = 2.3^{log x} ⇒ 5^{log x}. = 2.3^{log x} Hence, x = 10.

Mathematics

Solve for x: 5^{log x} + 3^{log x} = 3^{log x + 1} - 5^{log x - 1}.

Logarithms

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Mathematics

Solve for x: 5log x + 3log x = 3log x + 1 - 5log x - 1.

Logarithms

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