Solve 1000000 = 1.2 ^ (x - 1) | 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

$$1,000,000=1.20^{x-1}$$

Solve for x

$x=\log_{1.2}\left(1200000\right)\approx 76.775518819$

Steps Using Definition of Logarithm

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

$$1.2^{x-1}=1000000$$

Take the logarithm of both sides of the equation.

$$\log(1.2^{x-1})=\log(1000000)$$

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

$$\left(x-1\right)\log(1.2)=\log(1000000)$$

Divide both sides by $\log(1.2)$.

$$x-1=\frac{\log(1000000)}{\log(1.2)}$$

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

$$x-1=\log_{1.2}\left(1000000\right)$$

Add $1$ to both sides of the equation.

$$x=\frac{6\ln(10)}{\ln(\frac{6}{5})}-\left(-1\right)$$

Solve for x (complex solution)

$x=\frac{i\times 2\pi n_{1}}{\ln(1.2)}+\log_{1.2}\left(1200000\right)$
$n_{1}\in \mathrm{Z}$