What is x equal to in the equation log(105⋅10x)=12
?(1 point)
To solve for x in the equation log(105⋅10x)=12, we can start by using the property of logarithms that allows us to rewrite the equation as an exponential equation.
log(105⋅10x)=12 is equivalent to 105⋅10x = 10^12.
To simplify further, we can rewrite 10^12 as 1,000,000,000,000.
So, the equation becomes 105⋅10x = 1,000,000,000,000.
Now, we need to isolate x on one side of the equation.
Dividing both sides of the equation by 105, we get 10x = 1,000,000,000,000/105.
Simplifying the right side, 1,000,000,000,000 divided by 105 is 9,523,809,523.809.
Therefore, 10x = 9,523,809,523.809.
To solve for x, we need to take the logarithm of both sides.
log(10x) = log(9,523,809,523.809).
Now, we can solve for x using a logarithmic calculator or by using the property of logarithms that states log(ab) = log(a) + log(b).
We can rewrite the equation as x*log(10) = log(9,523,809,523.809).
Since log(10) is equal to 1, the equation simplifies to x = log(9,523,809,523.809).
Using a logarithmic calculator, we find that x is approximately 11.9797.
Therefore, x is approximately equal to 11.9797.