Student Question

`7^(3x+4)=49^(2x+1)` Solve the equation.

Expert Answers

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`7^(3x+4)=49^(2x+1)`

To solve, factor the 49.

`7^(3x+4)=(7^2)^(2x+1)`

To simplify the right side, apply the exponent property `(a^m)^n=a^(m*n)` .

`7^(3x+4)=7^(4x+2)`

Since the two sides have the same base, to solve for the value of x, set the exponent at the left equal to the exponent at the right side.

`3x + 4= 4x + 2`

`3x - 4x = 2 - 4`

`-x=-2`

`x=2`

Therefore, the solution is `x = 2` .

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