What is the answer to log_{10}(7x)=log_{10}(37)+5log_{10}(x) ?

The answer to log_{10}(7x)=log_{10}(37)+5log_{10}(x) is x= 1/(10^{(log_{10)(37)-log_{10}(7))/4}}

Solve for x: log_{10}(7x)=log_{10}(37)+5log_{10}(x)

The solution is x= 1/(10^{(log_{10)(37)-log_{10}(7))/4}}

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lo g_{10} (7 x) = lo g_{10} (37) + 5 lo g_{10} (x)

x = \frac{1}{1 0 ^{\frac{l o g _{10} ( 37 ) - l o g _{10} ( 7 )}{4}}}

Decimal

x = 0.65951 \dots

Solution steps

lo g_{10} (7 x) = lo g_{10} (37) + 5 lo g_{10} (x)

Apply log rules

x = \frac{1}{1 0 ^{\frac{l o g _{10} ( 37 ) - l o g _{10} ( 7 )}{4}}}

Verify Solutions:

x = \frac{1}{1 0 ^{\frac{l o g _{10} ( 37 ) - l o g _{10} ( 7 )}{4}}}

True

The solution is

x = \frac{1}{1 0 ^{\frac{l o g _{10} ( 37 ) - l o g _{10} ( 7 )}{4}}}

- 24 = 20 \cdot lo g_{10} (x)

0.189 = - lo g_{10} (x)

lo g_{3} (x^{2} + 2 x + 2) = 0

ln (x) + ln (x + 8) = 4

lo g_{33} (x) = 2

What is the answer to log_{10}(7x)=log_{10}(37)+5log_{10}(x) ?
The answer to log_{10}(7x)=log_{10}(37)+5log_{10}(x) is x= 1/(10^{(log_{10)(37)-log_{10}(7))/4}}
Solve for x: log_{10}(7x)=log_{10}(37)+5log_{10}(x)
The solution is x= 1/(10^{(log_{10)(37)-log_{10}(7))/4}}