Solving Logarithmic Equations Math Example 1

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easy

Solve

\log_2(x) = 5

1
Convert from logarithmic to exponential form: $\log_2(x) = 5$ means $2^5 = x$ .
2
Calculate: $x = 2^5 = 32$ .
3
Check: $\log_2(32) = \log_2(2^5) = 5$ . ✓

Answer

x = 32

The fundamental relationship between logarithms and exponents is:

\log_b(a) = c

if and only if

b^c = a

. Converting to exponential form is the most direct way to solve simple logarithmic equations.

About Solving Logarithmic Equations

Solving equations containing logarithms by converting to exponential form or using log properties to combine and simplify.

Solve [formula].

Solve [formula].

Solve [formula].