solve the following equation
9^x-1 = 144(6x)
please show work.
9x-1=144(6x)
9x-1=864x
9x-1-864x=0
you haven't written the question properly . Is the power of 9 the x-1?
To solve the equation 9^x-1 = 144(6x), we need to isolate the variable x. Let's break it down step by step:
Step 1: Distribute the 144 to the terms inside the parentheses.
9^x - 1 = 864x
Step 2: Move the constant term (-1) to the right side of the equation by adding 1 to both sides.
9^x = 864x + 1
Step 3: Now, let's take the logarithm of both sides. Any base can be used, but we typically use the natural logarithm (ln) or the base-10 logarithm (log).
ln(9^x) = ln(864x + 1)
Step 4: Apply the logarithmic property, which states that ln(a^b) = b * ln(a).
x * ln(9) = ln(864x + 1)
Step 5: Divide both sides of the equation by ln(9) to isolate x.
x = ln(864x + 1) / ln(9)
The equation is now solved, and x is in terms of logarithms.