log_b x=y ⇔ x= b^y
This definition tells us how to rewrite the logarithm equivalent of y in exponential form. The argument x is equal to b raised to the power of y.
In the given equation, -2 is the exponent to which 3 must be raised to obtain 2x-1. Now, let's solve our equation.
We found that x= 59 is the answer to the given equation.
b To solve the given logarithmic equation, we will use the fact a logarithm is the inverse of an exponential function. Make sure that the base of the logarithm and the exponential expression are the same.
5^(log_5 ( x)) = 3
In our case, log_5 ( x) is the exponent to which 5 must be raised to result in the desired number. Because 5 raised to this exponent must be equal to 3, we have that x must be equal to 3.
5^(log_5 ( x)) = 3
⇕
x = 3
log_b m - log_b n = log_b mn
First, we can use the above property to isolate the variable from the logarithm. Then, we will write the right-hand side as a logarithm.
Next, we will use the fact that if two equivalent logarithmic expressions have the same base, then the arguments must be equal.
log_b x=log_b y ⇔ x= y
Let's apply the above property to our equation.
We want to use the Change of Base Formula to solve the given logarithmic equation.
log_b m = log_c m/log_c b
In the above formula m, b, and c are positive numbers, with b≠ 1 and c≠ 1. We will apply this formula to the expression on the left-hand side of the equation.
log_3 ( 5) = log 5/log 3
Recall that if the base of a logarithm is not stated, it is 10. For example, log 5 = log_(10) 5. Logarithms with this base are called common logarithms, and can be found using a calculator.
