Question

To solve 49^3x = 343^2x+1, write each side of the equation in terms of base ____

Answer 1

Create equivalent expressions in the equation that all have equal bases.72(3x)=73(2x+1)72(3x)=73(2x+1)Since the bases are the same, then two expressions are only equal if the exponents are also equal.2(3x)=3(2x+1)

Answer 2

Each side of $49^{3x} = 343^{2x + 1}$, expressed in terms of their bases, is: $7^{2(3x)} = 7^{3(2x + 1)}$.

Solving Equations by Expressing Equations in Terms of their Bases

To solve an equation, the bases can be made equivalent and cancelled out by creating exponents.

Given:

$49^{3x} = 343^{2x + 1}$

First, express each side by simplifying their bases and make them equivalent. Let the base be 7.

Thus:

$7^{2(3x)} = 7^{3(2x + 1)}$

To solve, cancel the bases to have, 2(3x) = 3(2x + 1) and solve for x.

Therefore, each side of $49^{3x} = 343^{2x + 1}$, expressed in terms of their bases, is: $7^{2(3x)} = 7^{3(2x + 1)}$.

Learn more about bases on:

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