Solve (5)^(2y)=25THEN(5)^(-y) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$${ 5 }^{ 2y } =25THEN { 5 }^{ -y }$$

Solve for E

$E=\frac{125^{y}}{25HNT}$
$N\neq 0\text{ and }H\neq 0\text{ and }T\neq 0$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$25THEN\times 5^{-y}=5^{2y}$$

The equation is in standard form.

$$\frac{25HNT}{5^{y}}E=25^{y}$$

Divide both sides by $25THN\times 5^{-y}$.

$$\frac{\frac{25HNT}{5^{y}}E\times 5^{y}}{25HNT}=\frac{25^{y}\times 5^{y}}{25HNT}$$

Dividing by $25THN\times 5^{-y}$ undoes the multiplication by $25THN\times 5^{-y}$.

$$E=\frac{25^{y}\times 5^{y}}{25HNT}$$

Divide $25^{y}$ by $25THN\times 5^{-y}$.

$$E=\frac{125^{y}}{25HNT}$$

Solve for H

$H=\frac{125^{y}}{25ENT}$
$N\neq 0\text{ and }E\neq 0\text{ and }T\neq 0$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$25THEN\times 5^{-y}=5^{2y}$$

The equation is in standard form.

$$\frac{25ENT}{5^{y}}H=25^{y}$$

Divide both sides by $25TEN\times 5^{-y}$.

$$\frac{\frac{25ENT}{5^{y}}H\times 5^{y}}{25ENT}=\frac{25^{y}\times 5^{y}}{25ENT}$$

Dividing by $25TEN\times 5^{-y}$ undoes the multiplication by $25TEN\times 5^{-y}$.

$$H=\frac{25^{y}\times 5^{y}}{25ENT}$$

Divide $25^{y}$ by $25TEN\times 5^{-y}$.

$$H=\frac{125^{y}}{25ENT}$$