Question

If x + log10(1 + 2x) = xlog10 5 + log10 6 then x is equal to (a) 2, –3 (b) 2 only (c) 1 (d) 3

Answer 1

answer is option C
hope it helps : )

Answer 2

Option C

The value of x=1.

Step-by-step explanation:

Given:

$\rightarrow \: x + log_{10}(1 + 2x) = x log_{10}(5) + log_{10}(6) \\ \rightarrow \: x log_{10}(10) + log_{10}(1 + 2x) = log_{10}( {5}^{x} ) + log_{10}(6) \\ \rightarrow \: log_{10}( {10}^{x} ) + log_{10}(1 + 2x) = log_{10}(6 \times {5}^{x} ) \\ \rightarrow \: log_{10}(({10}^{x})(1 + 2x)) = log_{10}(6 \times {5}^{x} ) \\ \rightarrow \: ({10}^{x})(1 + 2x) = 6 \times {5}^{x} \: \\ \rightarrow \: ({5}^{x})( {2}^{x} ) (1 + 2x)= 6 \times {5}^{x} \\ \rightarrow \: ({2}^{x})(1 + 2x) = 6$

For x=1, LHS = RHS.

The value of x=1.