What is the answer to log_{5}(x)=1+log_{10}(x^{25}) ?

The answer to log_{5}(x)=1+log_{10}(x^{25}) is x=10^{(log_{10}(5))/(1-25log_{10)(5)}}

Solve for x: log_{5}(x)=1+log_{10}(x^{25})

The solution is x=10^{(log_{10}(5))/(1-25log_{10)(5)}}

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lo g_{5} (x) = 1 + lo g_{10} (x^{25})

x = 1 0^{\frac{l o g _{10} ( 5 )}{1 - 25 l o g _{10} ( 5 )}}

Decimal Notation

x = 0.90692 \dots

Solution steps

lo g_{5} (x) = 1 + lo g_{10} (x^{25})

Apply log rules

x = 1 0^{\frac{l o g _{10} ( 5 )}{1 - 25 l o g _{10} ( 5 )}}

Verify Solutions:

x = 1 0^{\frac{l o g _{10} ( 5 )}{1 - 25 l o g _{10} ( 5 )}}

True

The solution is

x = 1 0^{\frac{l o g _{10} ( 5 )}{1 - 25 l o g _{10} ( 5 )}}

\frac{x}{lo g _{2} ( 4 x - 12 )} = 5

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

ln (x + 2) = 2 + ln (x)

ln (5 + e^{- 2} x) = 3

2 \cdot (lo g_{5} (x))^{2} + 3 = 7 \cdot lo g_{5} (x)

What is the answer to log_{5}(x)=1+log_{10}(x^{25}) ?
The answer to log_{5}(x)=1+log_{10}(x^{25}) is x=10^{(log_{10}(5))/(1-25log_{10)(5)}}
Solve for x: log_{5}(x)=1+log_{10}(x^{25})
The solution is x=10^{(log_{10}(5))/(1-25log_{10)(5)}}