the base of exponential solve 14^(14x+1)=5^x, but the bases are not equal. the eq. has solutions? Solution 14^(14x+1) = 5^x To solve, we will apply the logarithm to both sides. ==> log 14^(14x+1) = log 5^x Now we will use the logarithm properties to solve. We know that log a^b = b^log a ==> (14x+1)*log 14 = x *log 5 Now we will divide by log14*x ==> (14x+1)/x = log5/log14 ==> 14 + 1/x = log5/log14 ==> 1/x = log5/log14 - 14 = -13.39 ==> x = 1/-13.39 = -0.0746 ==> Then, the solution for the equation is x = -0.0746.

1. the base of exponential
solve 14^(14x+1)=5^x, but the bases are not equal.
the eq. has solutions?
Solution
14^(14x+1) = 5^x
To solve, we will apply the logarithm to both sides.
==> log 14^(14x+1) = log 5^x
Now we will use the logarithm properties to solve.
We know that log a^b = b^log a
==> (14x+1)*log 14 = x *log 5
Now we will divide by log14*x
==> (14x+1)/x = log5/log14
==> 14 + 1/x = log5/log14
==> 1/x = log5/log14 - 14
= -13.39
==> x = 1/-13.39 = -0.0746
==> Then, the solution for the equation is x = -0.0746