write the expression as the logarithm of a single quantity.
2 In 8 + 5 In z
My answer is 7 In 8z but I don't not think this is right!
Nope, not right.
try these rules...
a ln b= ln( b^a)
and ln c + ln d= ln (cd).
use the properties of logarithms to simplify the logarithmic expression.
log10 (9/300)
Please explain!!
To write the expression 2 ln(8) + 5 ln(z) as the logarithm of a single quantity, you can use the properties of logarithms.
Let's break it down step by step:
Step 1: Apply the power rule of logarithms
2 ln(8) becomes ln(8^2), and 5 ln(z) becomes ln(z^5).
So, the expression simplifies to ln(8^2) + ln(z^5).
Step 2: Apply the product rule of logarithms
When adding logarithms with the same base, it can be combined into a single logarithm by multiplying the arguments.
ln(8^2) + ln(z^5) becomes ln(8^2 * z^5).
Step 3: Simplify the expression
ln(8^2 * z^5) can be further simplified by calculating the value inside the logarithm.
8^2 * z^5 equals (8 * 8) * (z * z * z * z * z).
This simplifies to 64z^5, so the final expression is:
ln(64z^5).