Can someone show me the steps for solving this logarithm?
log4x+log412=log<sub448
Thanks!
EDIT:
It's log4x+log412=log448
recall log (AB) = log A + log B
so log4x + log412 = log448 becomes
log4(12x) = log448
then
12x = 48
x = 4
Of course! To solve the logarithmic equation log4x + log412 = log448, we can use logarithmic properties to simplify the equation and then solve for x. Here are the steps:
Step 1: Use the logarithmic property logb(xy) = logbx + logby to combine the two logarithms on the left side of the equation.
So, we have log4(x * 12) = log448.
Step 2: Simplify the equation further by applying another logarithmic property logbba = a.
In this case, we can simplify the equation to x * 12 = 48.
Step 3: Solve the resulting equation for x by isolating the variable. Divide both sides of the equation by 12:
x = 48 / 12.
Simplifying further, we get:
x = 4.
Therefore, the solution to the given logarithmic equation is x = 4.
I hope this explanation helps! Let me know if you have any further questions.