Solve 70=90*3^-25x+50

$$70 = 90 \times 3 ^ { - 25 x } + 50$$

Solve for x

$$x=\frac{-\log_{3}\left(2\right)+2}{25}\approx 0.05476281$$

Steps Using Definition of Logarithm

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

$$90\times 3^{-25x}+50=70$$

Subtract 50 from both sides of the equation.

$$90\times 3^{-25x}=20$$

Divide both sides by 90.

$$3^{-25x}=\frac{2}{9}$$

Take the logarithm of both sides of the equation.

$$\log(3^{-25x})=\log(\frac{2}{9})$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$-25x\log(3)=\log(\frac{2}{9})$$

Divide both sides by \log(3).

$$-25x=\frac{\log(\frac{2}{9})}{\log(3)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$-25x=\log_{3}\left(\frac{2}{9}\right)$$

Divide both sides by -25.

$$x=\frac{\log_{3}\left(2\right)-2}{-25}$$

Solve for x (complex solution)

$$x=-\frac{2\pi n_{1}i}{25\ln(3)}-\frac{\log_{3}\left(2\right)}{25}+\frac{2}{25}$$

$$n_{1}\in \mathrm{Z}$$