What is the answer to log_{10}(10^x+2)=2x+1 ?

The answer to log_{10}(10^x+2)=2x+1 is x=-(ln(2))/(ln(10))

Solve for x: log_{10}(10^x+2)=2x+1

The solution is x=-(ln(2))/(ln(10))

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lo g_{10} (1 0^{x} + 2) = 2 x + 1

x = - \frac{ln ( 2 )}{ln ( 10 )}

Decimal

x = - 0.30102 \dots

Solution steps

lo g_{10} (1 0^{x} + 2) = 2 x + 1

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

1 0^{l o g_{10} (1 0^{x} + 2)} = 1 0^{2 x + 1}

Simplify

1 0^{l o g_{10} (1 0^{x} + 2)} : 1 0^{x} + 2

1 0^{x} + 2 = 1 0^{2 x + 1}

Solve

1 0^{x} + 2 = 1 0^{2 x + 1} : x = - \frac{ln ( 2 )}{ln ( 10 )}

x = - \frac{ln ( 2 )}{ln ( 10 )}

Verify Solutions:

x = - \frac{ln ( 2 )}{ln ( 10 )}

True

The solution is

x = - \frac{ln ( 2 )}{ln ( 10 )}

lo g_{10} (x) = - 1.5

3 lo g_{10} (2 x + 6) = 6

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

ln (x + 2) = - 5

- 1 = 2 lo g_{\frac{1}{4}} (x)

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