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

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

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

The solution is x=1,x= 1/10 ,x=10

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\frac{lo g _{10} ( x ^{3} )}{3} = (lo g_{10} (x))^{3}

x = 1, x = \frac{1}{10}, x = 10

Decimal

x = 1, x = 0.1, x = 10

Solution steps

\frac{lo g _{10} ( x ^{3} )}{3} = (lo g_{10} (x))^{3}

Multiply both sides by

3

\frac{lo g _{10} ( x ^{3} )}{3} \cdot 3 = (lo g_{10} (x))^{3} \cdot 3

Simplify

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

Apply log rules

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

Rewrite the equation with

lo g_{10} (x) = u

u = u^{3}

Solve

u = u^{3} : u = 0, u = - 1, u = 1

u = 0, u = - 1, u = 1

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

lo g_{10} (x) = 0 : x = 1

Solve

lo g_{10} (x) = - 1 : x = \frac{1}{10}

Solve

lo g_{10} (x) = 1 : x = 10

x = 1, x = \frac{1}{10}, x = 10

Verify Solutions:

x = 1

True

, x = \frac{1}{10}

True

, x = 10

True

The solutions are

x = 1, x = \frac{1}{10}, x = 10

1.5 lo g_{x} (9) = 3

12.4 = - lo g_{10} (x)

lo g_{4} (2 x + 10) = 2

lo g_{4} (x + 4) = - 3

lo g_{2} (x - 3) = 6

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