3^x.5^x+1=20 solve x
3^x * 5^x + 1=20
(3*5)^x = 19
15^x = 19
x = log1519
(3^x)(5^x) + 1 = 20
(15)^x = 19
use logs
x log15 = log 19
x = log19/log15 = appr 1.08729
Use your calculator to check, it works
To solve for x in the equation 3^x * 0.5^(x+1) = 20, let's break it down step by step:
Step 1: Start by isolating one of the bases, either 3 or 0.5, by moving the other base to the other side of the equation. Let's choose to isolate 3.
Divide both sides of the equation by 0.5^(x+1):
(3^x) = 20 / (0.5^(x+1))
Step 2: Simplify the right side of the equation by evaluating the value of 0.5^(x+1). Recall that any number raised to the power of 0 is equal to 1, and any number raised to the power of 1 is equal to itself.
0.5^(x+1) = 0.5^x * 0.5^1 = 0.5^x * 0.5 = 0.5^(x+1) = 1/2 * 1/2 = 1/4
Now, the equation becomes:
3^x = 20 / (1/4)
Step 3: Simplify further by dividing 20 by 1/4:
3^x = 20 * 4 = 80
Step 4: Rewrite the equation in exponential form by converting 3^x into a logarithm.
Take the logarithm (base 3) of both sides of the equation:
log3(3^x) = log3(80)
Step 5: Simplify the left side of the equation using the exponent rule of logarithms.
x = log3(80)
Step 6: Use a calculator to find the approximate value of x.
x ≈ 3.144
Therefore, the solution to the equation 3^x * 0.5^(x+1) = 20 is approximately x = 3.144.