What is the value of x in 2(5^x)=14? A. log5/log7 B. log7-log5 C. log7/log5 D. log2

Question

asked Apr 12, 2024 78.3k views

1 Answer

German Alfonso · Answer 1 · 2024-04-16T21:18:02+0000

Answer:

$\textsf{C)} \quad (\log7)/(\log5)$

Explanation:

Given equation:

$2\left(5^x\right)=14$

Isolate the exponential term by dividing both sides of the equation by 2:

$(2\left(5^x\right))/(2)=(14)/(2)$

5^x=7

$\textsf{Apply the log law:} \quad a^c=b \iff \log_ab=c$

$\log_57=x$

$x=\log_57$

$\textsf{Apply the change of base rule}, \; \log_ab=(\log_nb)/(\log_na),\;\textsf{where the new base is 10:}$

$x=\log_57=(\log_(10)7)/(\log_(10)5)$

As log without a specified base is usually assumed to be the logarithm with base 10, we can write the value of x as:

$x=(\log7)/(\log5)$