The problem is to solve the equation $\log(x) = 3$. The logarithm is base 10.

AlgebraLogarithmsExponential EquationsSolving Equations
2025/5/2

1. Problem Description

The problem is to solve the equation log(x)=3\log(x) = 3. The logarithm is base
1
0.

2. Solution Steps

To solve the equation log(x)=3\log(x) = 3, we need to rewrite the equation in exponential form. Since the logarithm is base 10, the equation can be rewritten as:
103=x10^3 = x
Calculating 10310^3:
103=10×10×10=100010^3 = 10 \times 10 \times 10 = 1000
Therefore, x=1000x = 1000.

3. Final Answer

x=1000x = 1000

Related problems in "Algebra"

The problem describes a quadratic number pattern $4, p, 11, q, 22, ...$ with a constant second diffe...

SequencesQuadratic SequencesPatternsGeneral TermQuadratic Equations
2025/5/2

The problem asks us to solve the equation $\ln(x+2) + \ln(x) = \ln(x+30)$ for $x$.

LogarithmsEquationsQuadratic EquationsSolving EquationsAlgebraic Manipulation
2025/5/2

Pedro is 4 years older than Juan. Five times Juan's age is three times Pedro's age. What are their ...

Linear EquationsWord ProblemSystems of Equations
2025/5/2

We are given the following information about a triangle: - The longest side is 8 cm longer than side...

TrianglePerimeterLinear EquationsWord Problem
2025/5/2

The problem asks us to solve for $x$ in two equations: a) $\frac{a}{x} = \frac{b}{c}$ b) $\frac{ab}{...

EquationsSolving for xLinear EquationsCross-multiplication
2025/5/2

The problem provides the formula $\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}$ and asks to solve f...

Equation SolvingFormula ManipulationReciprocals
2025/5/2

The problem consists of two parts. Part g) asks us to solve the equation $\frac{x}{5-y} = m-1$ for $...

Equation SolvingLinear EquationsVariable Isolation
2025/5/2

Solve the equation $\frac{2n}{x-4} = m$ for $x$.

Linear EquationsVariable SolvingEquation Manipulation
2025/5/2

Solve for $y$ in the equation $x+5 = \frac{3m}{y}$.

Equation SolvingAlgebraic ManipulationVariables
2025/5/2

We are given several equations and asked to isolate a specified variable in each. c) $\frac{ax}{y} =...

Equation SolvingVariable IsolationAlgebraic Manipulation
2025/5/2