What is the answer to log_{2}(x^5)=log_{10}(2x)^4 ?

The answer to log_{2}(x^5)=log_{10}(2x)^4 is x=1.00114…,x=138.33967…

Solve for x: log_{2}(x^5)=log_{10}(2x)^4

The solution is x=1.00114…,x=138.33967…

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lo g_{2} (x^{5}) = lo g_{10} (2 x)^{4}

x = 1.00114 \dots, x = 138.33967 \dots

Solution steps

lo g_{2} (x^{5}) = lo g_{10} (2 x)^{4}

Apply log rules

\frac{5 lo g _{10} ( x )}{lo g _{10} ( 2 )} = (lo g_{10} (2) + lo g_{10} (x))^{4}

Rewrite the equation with

lo g_{10} (x) = u

\frac{5 u}{lo g _{10} ( 2 )} = (lo g_{10} (2) + u)^{4}

Solve

\frac{5 u}{lo g _{10} ( 2 )} = (lo g_{10} (2) + u)^{4} : u \approx 0.00049 \dots, u \approx 2.14094 \dots

u \approx 0.00049 \dots, u \approx 2.14094 \dots

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

lo g_{10} (x) = 0.00049 \dots : x = 1.00114 \dots

Solve

lo g_{10} (x) = 2.14094 \dots : x = 138.33967 \dots

x = 1.00114 \dots, x = 138.33967 \dots

Verify Solutions:

x = 1.00114 \dots

True

, x = 138.33967 \dots

True

The solutions are

x = 1.00114 \dots, x = 138.33967 \dots

lo g_{5} (x^{2}) - 4 = 2 + ∣ lo g_{5} (x) - 3 ∣

lo g_{2} (x^{2}) = 8

lo g_{2} (x^{2}) = 2

lo g_{4} (2 x + 1) = 0

lo g_{10} (y) = \frac{1}{2}

What is the answer to log_{2}(x^5)=log_{10}(2x)^4 ?
The answer to log_{2}(x^5)=log_{10}(2x)^4 is x=1.00114…,x=138.33967…
Solve for x: log_{2}(x^5)=log_{10}(2x)^4
The solution is x=1.00114…,x=138.33967…