Solve
Log base 10^x=4
your notation is bogus.
log base 10 (x) = 4
x = 10^4 = 10000
If that's not what you wanted, then 'splain what you mean. As written, you haven't specified a base. Just that you want the log of 10^x.
Take a look at other posted problems involving logs to see how to write it so we understand what you mean.
log10^x=4
the 10 is under the log
In that case, it's what I wrote above. Ditch the ^; it doesn't mean anything
assuming base 10,
log x = 4
means that 4 is the power of 10 needed to get x. 10^4 = 10,000 so log x = 4
Using base 3, log81 = 4 because 3^4 = 81
Log and ^ are inverse operations.
square root and square are inverses:
√x=5 means x = 5^2
multiplication and division are inverses:
x/3 = 5 means x = 3*5
addition/subtraction are inverses:
x-3 = 10 means x = 10+3
so, don't be stumped by logs; they're just powers written on the other side of the equation
log2 (3x-1) = 8
means 3x-1 = 2^8
hang in there. I almost flunked my first test on logs. The book kept saying " a logarithm is an exponent" and I thought, "What? Just look at it -- it's nothing like an exponent!" Then a few days later it all clicked.
Okay thank you for the explanation!! Logarithms are difficult and get some use to.
To solve the equation, we will use the basic properties of logarithms.
The equation is given as log base 10 of x equals 4.
This can be expressed as:
log₁₀(x) = 4
To isolate x, we will use the definition of logarithms.
In logarithmic form, the equation log base b of a equals c is equivalent to b raised to the power of c equals a.
Applying this definition to our equation, we get:
10^4 = x
Evaluating 10^4, we find that it is equal to 10,000.
So, x = 10,000.
Therefore, the solution to the equation is x = 10,000.