What is the answer to 81^{log_{10}(9x)}=x^2 ?

The answer to 81^{log_{10}(9x)}=x^2 is x= 1/(10^{(4log_{10)(3)^2)/(2log_{10)(3)-1}}}

Solve for x: 81^{log_{10}(9x)}=x^2

The solution is x= 1/(10^{(4log_{10)(3)^2)/(2log_{10)(3)-1}}}

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8 1^{l o g_{10} (9 x)} = x^{2}

x = \frac{1}{1 0 ^{\frac{4 l o g _{10} ( 3 ) ^{2}}{2 l o g _{10} ( 3 ) - 1}}}

Decimal Notation

x = 7.94516 E 19

Solution steps

8 1^{l o g_{10} (9 x)} = x^{2}

Apply log rules

x = \frac{1}{1 0 ^{\frac{4 l o g _{10} ( 3 ) ^{2}}{2 l o g _{10} ( 3 ) - 1}}}

Verify Solutions:

x = \frac{1}{1 0 ^{\frac{4 l o g _{10} ( 3 ) ^{2}}{2 l o g _{10} ( 3 ) - 1}}}

True

The solution is

x = \frac{1}{1 0 ^{\frac{4 l o g _{10} ( 3 ) ^{2}}{2 l o g _{10} ( 3 ) - 1}}}

lo g_{3} (3 x) = 2

0 = 2 x ln (\frac{x}{2}) + x

4 - 2 \cdot lo g_{3} (x) = 3

2 lo g_{7} (2 x - 1) - 5 = 9

ln (c) + ln (c) = 1

What is the answer to 81^{log_{10}(9x)}=x^2 ?
The answer to 81^{log_{10}(9x)}=x^2 is x= 1/(10^{(4log_{10)(3)^2)/(2log_{10)(3)-1}}}
Solve for x: 81^{log_{10}(9x)}=x^2
The solution is x= 1/(10^{(4log_{10)(3)^2)/(2log_{10)(3)-1}}}