What is the answer to x^{log_{10}(4x)}=256 ?

The answer to x^{log_{10}(4x)}=256 is

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x^{log_{10}(4x)}=256

x^{l o g_{10} (4 x)} = 256

x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) + 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}, x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) - 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}

Decimal Notation

x = 19.04355 \dots, x = 0.01312 \dots

Solution steps

x^{l o g_{10} (4 x)} = 256

Apply exponent rules

lo g_{10} (4 x) ln (x) = ln (256)

Solve

lo g_{10} (4 x) ln (x) = ln (256) : x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) + 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}, x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) - 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}

x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) + 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}, x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) - 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}

Verify Solutions:

x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) + 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}

True

, x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) - 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}

True

The solutions are

x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) + 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}, x = 1 0^{\frac{- 2 l o g _{10} ( 2 ) - 4 l o g _{10} ( 2 ) ^{2} + \frac{32 l n ( 2 )}{l n ( 10 )}}{2}}

i, x^{i} = 2

9^{x} = 2 7^{x}

(\frac{1}{3})^{2 x + 5} = 2 7^{1 - x}

x, 8 \cdot 2^{6} = 2^{x}

What is the answer to x^{log_{10}(4x)}=256 ?
The answer to x^{log_{10}(4x)}=256 is
Solve for x: x^{log_{10}(4x)}=256
The solution is