The value of x is -1 after applying the exponent properties, the answer should be -1
It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\log_ac =b[/tex]
We have:
[tex]\rm 2log(x+11) = (1/2)^x[/tex]
[tex]\rm log(x+11) = (1/2)(1/2)^x\\\\\rm log(x+11) = (\dfrac{1}{2})^{1+x}\\\\\\\rm (x+11) = 10^{(\dfrac{1}{2})^{1+x}}\\\\\\[/tex]
Here the base is 10 and an exponent of 10 will give a multiple of 10 so the value of x+1 should be 10
x + 11 = 10
x = -1
Thus, the value of x is -1 after applying the exponent properties, the answer should be -1
Learn more about the Logarithm here:
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