Question

if 5 power x minus 5 power x minus 1 is equal to 100 find value of x​

Answer 1

Answer:

$\green{5^x-5^{x-1}=100\quad :\quad x=3}$

Step-by-step explanation:

$5^x-5^{x-1}=100$

$\black{\mathrm{Factor\:}5^x-5^{x-1}:}$

$5^x-5^{x-1}$

$\gray{5^x=5^{x-1+1}}$

$=5^{x-1+1}-5^{x-1}$

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c}$

$\gray{5^{x-1+1}=5^1\cdot \:5^{x-1}}$

$=5^1\cdot \:5^{x-1}-5^{x-1}$

$\gray{\mathrm{Factor\:out\:common\:term\:}5^{x-1}}$

$=5^{x-1}\left(5^1-1\right)$

$\gray{\mathrm{Refine}}$

$=4\cdot \:5^{x-1}$

$4\cdot \:5^{x-1}=100$

$\gray{\mathrm{Divide\:both\:sides\:by\:}4}$

$\frac{4\cdot \:5^{x-1}}{4}=\frac{100}{4}$

$\gray{\mathrm{Simplify}}$

$5^{x-1}=25$

$\gray{\mathrm{Convert\:}25\mathrm{\:to\:base\:}5}$

$\gray{25=5^2}$

$5^{x-1}=5^2$

$\gray{\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g\left(x\right)}$

$x-1=2$

$\black{\mathrm{Solve\:}\:x-1=2:}$

$x-1=2$

$\gray{\mathrm{Add\:}1\mathrm{\:to\:both\:sides}}$

$x-1+1=2+1$

$\gray{\mathrm{Simplify}}$

$x=3$

Answer 2

Answer:

the answer will be 3 .(x is equal to 3)