Solve Logarithmic Equation: 3 log x = 1/9 - Math Solver AI

$Math Problem$

Mathematics Grade 10 (Junior High)

Question Content

Solve the equation: 3 log x = 1/9

Correct Answer

x = 10^(1/27) ≈ 1.030

Detailed Solution Steps

1
Step 1: Isolate log x: log x = (1/9)/3 = 1/27.
2
Step 2: Convert to exponential form (base 10, since no base is specified): x = 10^(1/27).
3
Step 3: Optional: Calculate the decimal approximation using a calculator: 10^(1/27) ≈ 1.030.

Knowledge Points Involved

1

Basic Logarithm Isolation

To solve for x in k log_a x = b, first isolate log_a x = b/k, then convert to exponential form x = a^(b/k).

2

Logarithm to Exponential Conversion

If log_a x = c, then x = a^c for a>0, a≠1, x>0. Converts logarithmic equations to exponential form to solve for the variable inside the logarithm.

3

Decimal Approximations of Logarithmic Solutions

When the solution is an exponential term with a fractional exponent, use a calculator and the change of base formula to find a decimal approximation if needed.

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