Solve 7(x^1-2)=5(3^4x+1)

$$7 ( x ^ { 1 } - 2 ) = 5 ( 3 ^ { 4 } x + 1 )$$

Solve for x

$$x=-\frac{19}{398}\approx -0.047738693$$

Steps for Solving Linear Equation

Calculate x to the power of 1 and get x.

$$7\left(x-2\right)=5\left(3^{4}x+1\right)$$

Use the distributive property to multiply 7 by x-2.

$$7x-14=5\left(3^{4}x+1\right)$$

Calculate 3 to the power of 4 and get 81.

$$7x-14=5\left(81x+1\right)$$

Use the distributive property to multiply 5 by 81x+1.

$$7x-14=405x+5$$

Subtract 405x from both sides.

$$7x-14-405x=5$$

Combine 7x and -405x to get -398x.

$$-398x-14=5$$

Add 14 to both sides.

$$-398x=5+14$$

Add 5 and 14 to get 19.

$$-398x=19$$

Divide both sides by -398.

$$x=\frac{19}{-398}$$

Fraction \frac{19}{-398} can be rewritten as -\frac{19}{398} by extracting the negative sign.

$$x=-\frac{19}{398}$$