Solve (10 ^ 6) / (100 ^ 2) = 10 ^ x | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

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

a⋅(b-2)=3b

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

a⋅(b-2)=3b

Question

$$10^{6}\div100^{2}=10^{x}$$

Solve for x

$x=2$

Steps Using Definition of Logarithm

Calculate $10$ to the power of $6$ and get $1000000$.

$$\frac{1000000}{100^{2}}=10^{x}$$

Calculate $100$ to the power of $2$ and get $10000$.

$$\frac{1000000}{10000}=10^{x}$$

Divide $1000000$ by $10000$ to get $100$.

$$100=10^{x}$$

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

$$10^{x}=100$$

Take the logarithm of both sides of the equation.

$$\log(10^{x})=\log(100)$$

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

$$x\log(10)=\log(100)$$

Solve for x (complex solution)

$x=2+2\pi n_{1}i\log(e)$
$n_{1}\in \mathrm{Z}$