Solve $$ \log _{5}(5 x+2)=1 $$

To solve the equation $$ \log _{5}(5x + 2) = 1 $$, follow these steps: 1. **Understand the logarithmic equation**: The equation $$ \log_b(a) = c $$ can be rewritten in its exponential form as $$ b^c = a $$. 2. **Apply the exponential form**: \[ \log _{5}(5x + 2) = 1 \quad \Rightarrow \quad 5^1 = 5x + 2 \] Simplifying the left side: \[ 5 = 5x + 2 \] 3. **Solve for $$ x $$**: \[ 5x + 2 = 5 \] Subtract 2 from both sides: \[ 5x = 3 \] Divide both sides by 5: \[ x = \frac{3}{5} \] **Final Answer:** $$ x = \dfrac{3}{5} $$ $$ x = \frac{3}{5} $$

Ask AI
Tools
- Math Solver
  
  Pre Algebra
  
  Fractions
  
  Decimals
  
  Exponents
  
  Radicals
  
  Ratios
  
  Integer
  
  Percent
  
  Algebra
  
  Equations
  
  Expressions
  
  Inequalities
  
  Functions
  
  Sequences
  
  Logarithmic
  
  Complex Numbers
  
  Matrices
  
  Pre Calculus
  
  Equations
  
  Inequalities
  
  Functions
  
  Calculus
  
  Derivatives
  
  Integrals
  
  Limits
  
  Series
  
  Trigonometry
  
  Equations
  
  Inequalities
  
  Functions
  
  Simplify
  
  Proof
  
  Geometry
  
  Statistics and Probability
  
  Matrix
- Calculators
  
  Geometry
  
  Perimeter & Area
  
  The Pythagorean Theorem
  
  Power of a Point Theorem
  
  Midpoint & Endpoint
  
  Statistic & Probability
  
  Standard Deviation
  
  Mean & Median & Mode & Range
  
  Algebra
  
  Ratio
  
  Slope
  
  Trigonometry
  
  Trigonometry Functions
  
  List of Trigonometric Identities
  
  Arithmetic
  
  Greatest Common Divisor & Least Common Multiple
  
  Percent & Decimal & Fraction
  
  Percentage
  
  Reduced Row Echelon Form (RREF)
Resources
- Question Bank
  
  Mathematics
  
  Arithmetic
  
  Pre Algebra
  
  Algebra
  
  Pre Calculus
  
  Calculus
  
  Geometry
  
  Statistics
  
  Probability
  
  Trigonometry
  
  Physics
  
  Chemistry
  
  Biology
  
  History
  
  Geography
  
  Economics
  
  English
  
  Everyday
  
  Arts
  
  Computer Technology
  
  Medicine
  
  Social Sciences
  
  Humanities
  
  Engineering
  
  Other
- Blog

Ask AI
Tools
- Math Solver
  - Pre Algebra
    - Fractions
    - Decimals
    - Exponents
    - Radicals
    - Ratios
    - Integer
    - Percent
  - Algebra
  - Pre Calculus
  - Calculus
    - Derivatives
    - Integrals
    - Limits
    - Series
  - Trigonometry
    - Equations
    - Inequalities
    - Functions
    - Simplify
    - Proof
  - Geometry
  - Statistics and Probability
  - Matrix
- Calculators
  - Geometry
  - Statistic & Probability
    - Standard Deviation
    - Mean & Median & Mode & Range
  - Algebra
    - Ratio
    - Slope
  - Trigonometry
    - Trigonometry Functions
    - List of Trigonometric Identities
  - Arithmetic
Resources
- Question Bank
  - Mathematics
    - Arithmetic
    - Pre Algebra
    - Algebra
    - Pre Calculus
    - Calculus
    - Geometry
    - Statistics
    - Probability
    - Trigonometry
  - Physics
  - Chemistry
  - Biology
  - History
  - Geography
  - Economics
  - English
  - Everyday
  - Arts
  - Computer Technology
  - Medicine
  - Social Sciences
  - Humanities
  - Engineering
  - Other
- Blog

Premium

Home Question Bank Math Algebra

Question

Solve

Ask by Higgins Griffin. in Canada

Jan 24,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Solution

To solve the equation

, follow these steps:

Understand the logarithmic equation: The equation can be rewritten in its exponential form as .
Apply the exponential form:

Simplifying the left side:
Solve for :

Subtract 2 from both sides:

Divide both sides by 5:

Final Answer:

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg

Explain

Simplify this solution

Bonus Knowledge

To solve the equation

, we start by using the definition of logarithms. The equation states that

This simplifies to:

Next, we subtract 2 from both sides:

This gives us:

Now, we divide both sides by 5:

Therefore, the solution to the equation

Latest Algebra Questions

Algebra Guam Mar 31, 2025

Prev Next