What is the answer to log_{10}(x^{64})=-3 ?

The answer to log_{10}(x^{64})=-3 is x= 1/(10^{3/64)},x=-1/(10^{3/64)}

Solve for x: log_{10}(x^{64})=-3

The solution is x= 1/(10^{3/64)},x=-1/(10^{3/64)}

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lo g_{10} (x^{64}) = - 3

x = \frac{1}{1 0 ^{\frac{3}{64}}}, x = - \frac{1}{1 0 ^{\frac{3}{64}}}

Decimal Notation

x = 0.89768 \dots, x = - 0.89768 \dots

Solution steps

lo g_{10} (x^{64}) = - 3

Apply exponent rule:

a^{2 \cdot n} = (a^{2})^{n}

x^{64} = (x^{2})^{32}

lo g_{10} ((x^{2})^{32}) = - 3

Apply log rules

x^{2} = \frac{1}{1 0 ^{\frac{3}{32}}}

Solve

x^{2} = \frac{1}{1 0 ^{\frac{3}{32}}} : x = \frac{1}{1 0 ^{\frac{3}{64}}}, x = - \frac{1}{1 0 ^{\frac{3}{64}}}

x = \frac{1}{1 0 ^{\frac{3}{64}}}, x = - \frac{1}{1 0 ^{\frac{3}{64}}}

Verify Solutions:

x = \frac{1}{1 0 ^{\frac{3}{64}}}

True

, x = - \frac{1}{1 0 ^{\frac{3}{64}}}

True

The solutions are

x = \frac{1}{1 0 ^{\frac{3}{64}}}, x = - \frac{1}{1 0 ^{\frac{3}{64}}}

lo g_{6} (7 x + 1) = 2

lo g_{5} (10) = lo g_{10} (x)

lo g_{a} (a^{n}) = n

lo g_{3} (x) = 3 - 2 lo g_{x} (3)

- 0.15 = lo g_{10} (x)

What is the answer to log_{10}(x^{64})=-3 ?
The answer to log_{10}(x^{64})=-3 is x= 1/(10^{3/64)},x=-1/(10^{3/64)}
Solve for x: log_{10}(x^{64})=-3
The solution is x= 1/(10^{3/64)},x=-1/(10^{3/64)}