What is the answer to log_{10}(2^x)=log_{10}(4^{x+2}) ?

The answer to log_{10}(2^x)=log_{10}(4^{x+2}) is x=-4

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log_{10}(2^x)=log_{10}(4^{x+2})

lo g_{10} (2^{x}) = lo g_{10} (4^{x + 2})

x = - 4

Solution steps

lo g_{10} (2^{x}) = lo g_{10} (4^{x + 2})

Apply log rules

2^{x} = 4^{x + 2}

Solve

2^{x} = 4^{x + 2} : x = - 4

x = - 4

Verify Solutions:

x = - 4

True

The solution is

x = - 4

lo g_{x} (0.015625) = 3

a, lo g_{ab} (a) = 3

lo g_{0.1} (x) = - 6

lo g_{\frac{1}{2}} (x + 1) = - 3

lo g_{5} (x) = 10

What is the answer to log_{10}(2^x)=log_{10}(4^{x+2}) ?
The answer to log_{10}(2^x)=log_{10}(4^{x+2}) is x=-4
Solve for x: log_{10}(2^x)=log_{10}(4^{x+2})
The solution is x=-4